Stokes Matrices for Frobenius Manifolds and the 6 Painlevé Equation - Davide Guzzetti (Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109, 2000)
These notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev'e equations.
Keywords: Painlevé equation

Super KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy - Gregorio Falqui; Cesare Reina; Alessandro Zampa (J. Geom. Phys. 35 (2000), no. 2-3, 239-272, 2000)

A Uniqueness Condition for Hyperbolic Systems of Conservation Laws - Alberto Bressan; Marta Lewicka (Discrete Contin. Dynam. Systems 6 (2000) 673-682, 2000)
Consider the Cauchy problem for a hyperbolic $n\\\\times n$ system of conservation laws in one space dimension: $$u_t+f(u)_x=0, u(0,x)=\\\\bar u(x).\\\\eqno(CP)$$ Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves.

Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities - Gianni Dal Maso; Helene Frankowska (ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393., 2000)

Well-posedness of the Cauchy problem for n x n systems of conservation laws - Alberto Bressan; Graziano Crasta; Benedetto Piccoli (Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p., 2000)

The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional - Matteo Negri (Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982, 1999)
We compute explicitly the anisotropy effect in the H1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations.

Approximation, Stability and control for Conservation Laws - Andrea Marson (SISSA, 1999)

Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains - Gianni Dal Maso; Igor V. Skrypnik (Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112, 1999)

A bihamiltonian approach to separation of variables in mechanics - Gregorio Falqui; Franco Magri; Marco Pedroni (Proceedings of the workshop on nonlinearity, integrability and all that : twenty years after NEEDS \\\'79, Lecce, Italy, July 1 - 10, 1999 / ed. by M. Boiti. - Singapore : World Scientific, 2000. - p. 258-266, 1999)
This paper is a report on a recent approach to the theory of separability of the Hamilton-Jacobi equations from the viewpoint of bihamiltonian geometry.

Blowup asymptotics for scalar conservation laws with a source - Helge Kristian Jenssen; Carlo Sinestrari (Comm. in Partial Differential Equations 24 (1999) 2237-2261, 1999)

The calibration method for the Mumford-Shah functional - Giovanni Alberti; Guy Bouchitte; Gianni Dal Maso (C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254, 1999)
In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3).

Categorial mirror symmetry for K3 surfaces - Claudio Bartocci; Ugo Bruzzo; Guido Sanguinetti (Comm. Math. Phys. 206 (1999) 265-272, 1999)
We study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$.

Correspondence between Minkowski and de Sitter quantum field theory - Marco Bertola; Gorini, Vittorio; Moschella, Ugo; Schaeffer, Richard (Phys. Lett. B, 1999)

Discrete approximation of the Mumford-Shah functional in dimension two - Antonin Chambolle; Gianni Dal Maso (M2AN 33 (1999) 651-672, 1999)

Enhanced gauge symmetries on elliptic K3 - Loriano Bonora; Cesare Reina; Alessandro Zampa (Phys.Lett. B452 (1999) 244-250, 1999)
We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s.

Evans-Vasilesco theorem in Dirichlet spaces - Gianni Dal Maso; Virginia De Cicco (Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15, 1999)

Extremal faces of the range of a vector measure and a theorem of Lyapunov - Stefano Bianchini (J. Math. Anal. Appl. 231 (1999) 301-318, 1999)

Frobenius manifolds and Virasoro constraints - Boris Dubrovin; Zhang Youjin (Selecta Math. (N.S.) 5 (1999) 423-466, 1999)
For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. Particularly, the genus $\\\\leq 1$ Virasoro conjecture of T.Eguchi, K.Hori, M.Jinzenji, and C.-S.Xiong and of S.Katz is proved for smooth projective varieties having semisimple quantum cohomology.

Hyperbolic Systems of Conservation Laws - Alberto Bressan (Rev. Mat. Complut. 12 (1999) 135-200, 1999)
This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions.

L-1 stability estimates for n x n conservation laws - Alberto Bressan; Tai-Ping Liu; Tong Yang (Arch. Ration. Mech. Anal. 149 (1999), no. 1, 1--22, 1999)
Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws, each characteristic field being linearly degenerate or genuinely nonlinear. In this paper we explicitly define a functional $\\\\Phi=\\\\Phi(u,v)$, equivalent to the $L^1$ distance, which is `almost decreasing\\\', i.e., $\\\\Phi(u(t),v(t))-\\\\Phi(u(s),v(s))\\\\leq\\\\break O (\\\\epsilon)·(t-s)$ for all $t>s\\\\geq 0$, for every pair of $\\\\epsilon$-approximate solutions $u,v$ with small total variation, generated by a wave-front-tracking algorithm. The small parameter $\\\\epsilon$ here controls the errors in the wave speeds, the maximum size of rarefaction fronts and the total strength of all non-physical waves in $u$ and in $v$. From the above estimate, it follows that front-tracking approximations converge to a unique limit solution, depending Lipschitz continuously on the initial data, in the $L^1$ norm. This provides a new proof of the existence of the standard Riemann semigroup generated by an $n\\\\times n$ system of conservation laws.\\\'\\\'

A Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient - Gianni Dal Maso; Vladimir V. Goncharov; Antonio Ornelas (Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717, 1999)
A constructive and improved version of the proof that there exist a continuous map that solves the convexified problem is presented. A Lipschitz continuous map is analyzed such that a map vector minimizes the functional at each vector satisfying Cellina\\\'s condition of existence of minimum. This map is explicitly given by a direct constructive algorithm.

The method of Poisson pairs in the theory of nonlinear PDEs - Gregorio Falqui; Franco Magri; Marco Pedroni (Direct and inverse methods in nonlinear evolution equations : Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999 / Robert Conte ... ; Antonio M. Greco ed. - Berlin : Springer, 2003. - (Lecture Notes in Physics ; 632), 1999)
The aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear partial differential equations. The prototype of these equations is the well-known Korteweg-de Vries (KdV) equation.\\nIn these lectures we touch the following subjects:\\ni) the birth and the role of the method of Poisson pairs inside the theory of the KdV equation;\\nii) the theoretical basis of the method of Poisson pairs;\\niii) the Gel\\\'fand-Zakharevich theory of integrable systems on bi-Hamiltonian manifolds;\\niv) the Hamiltonian interpretation of the Sato picture of the KdV flows and of its linearization on an infinite-dimensional Grassmannian manifold.\\nv) the reduction technique(s) and its use to construct classes of solutions;\\nvi) the role of the technique of separation of variables in the study of the reduced systems;\\nvii) some relations intertwining the method of Poisson pairs with the method of Lax pairs.

A multiplicity result for the Yamabe problem on $S\\\\sp n$ - Antonio Ambrosetti; Andrea Malchiodi (J. Funct. Anal. 168 (1999), no. 2, 529-561, 1999)
We prove a multiplicity result for the Yamabe problem on the manifold (S, g), where g is a perturbation of the standard metric g0 of Sn. Solutions are found by variational methods via an abstract perturbation result.

Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws - Debora Amadori; Paolo Baiti; Philippe G. LeFloch; Benedetto Piccoli (J. Differential Equations 151 (1999) 345-372, 1999)
The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.

A note on fractional KDV hierarchies. II. The bihamiltonian approach - Paolo Casati; Gregorio Falqui; Marco Pedroni (SISSA Library, 1999)

Oleinik type estimates and uniqueness for n x n conservation laws - Alberto Bressan; Paola Goatin (J. Differential Equations 156 (1999), no. 1, 26--49, 1999)
Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleĭnik in the scalar case.

Painlevé transcendents in two-dimensional topological field theory - Boris Dubrovin (The Painlevé property : one century later / Robert Conte ed. - New York : Springer-Verlag, 1999. - (CRM series in mathematical physics). - p. 287-412, 1999)

Perturbation of $Δ u+u^(N+2)/(N-2)=0$, the scalar curvature problem in $R^N$, and related topics - Antonio Ambrosetti; Jesus Garcia Azorero; Ireneo Peral (J. Funct. Anal. 165 (1999) 117-149, 1999)
Some nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

Projection singularities of extremals for planar systems - Ugo Boscain; Benedetto Piccoli (SISSA Library, 1999)

Recurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory - Boris Dubrovin; Andrei Ya A Maltsev (arXiv:solv-int/990400, 1999)
We present here the iteration procedure for the determination of free energy ǫ2-expansion using the theory of KdV - type equations. In our approach we use the conservation laws for KdV - type equations depending explicitly on times t1, t2, . . . to find the ǫ2-expansion of u(x, t1, t2, . . .) after the infinite number of shifts of u(x, 0, 0, . . .) ≡ x along t1, t2, . . . in recurrent form. The formulas for the free energy expansion are just obtained then as a result of quite simple integration procedure applied to un(x).

Renormalized solutions of elliptic equations with general measure data - Gianni Dal Maso; Francois Murat; Luigi Orsina; Alain Prignet (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808, 1999)

On the scalar curvature problem under symmetry - Antonio Ambrosetti; Andrea Malchiodi (SISSA Library, 1999)

Some properties of the solutions of obstacle problems with measure data - Paolo Dall'Aglio; Gianni Dal Maso (Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116, 1999)

Stokes matrices and monodromy of the quantum cohomology of projective spaces - Davide Guzzetti (Comm. Math. Phys. 207 (1999) 341-383, 1999)
n this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be formulated in a \\\"classical\\\" framework, as the problem of computation of Stokes matrices and monodromy of differential equations with regular and irregular singularities. We prove that the Stokes\\\' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups.

Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws - Alberto Bressan; Philippe G. LeFloch (Indiana Univ. Math. J. 48 (1999), no. 1, 43--84, 1999)
The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm.

Vanishing viscosity solutions of hyperbolic systems on manifolds - Stefano Bianchini; Alberto Bressan (SISSA Library, 1999)

Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case - Andrea Braides; Gianni Dal Maso; Adriana Garroni (Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58, 1999)
Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included.

The vector measures whose range is strictly convex - Stefano Bianchini; Carlo Mariconda (J. Math. Anal. Appl. 232 (1999) 1-19, 1999)

Algebraic Solutions to the Painlevé-VI Equation and Reflection Groups - Marta Mazzocco (SISSA, 1998)
Keywords: Painlevé VI equation

Asymptotic behavior of nonlinear Dirichlet problems in perforated domains - Gianni Dal Maso; Igor V. Skrypnik (Ann. Mat. Pura Appl. (4) 174 (1998), 13--72, 1998)

Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation - Boris Dubrovin; Zhang Youjin (Comm. Math. Phys. 198 (1998) 311-361, 1998)
We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov - Witten invariants via tau-function of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity.

Branching points for a class of variational operators - Antonio Ambrosetti (J. Anal. Math. 76 (1998) 321-335, 1998)

On the Cauchy Problem for the Whitham Equations - Tamara Grava (SISSA, 1998)
Keywords: Korteweg de Vries equation

Differential geometry of the space of orbits of a Coxeter group - Boris Dubrovin (J. Differential Geometry Suppl.4 (1998) 181-211, 1998)
Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\\\\\\\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group.

Diffusion of a particle in presence of N moving point sources - Gianfausto Dell'Antonio; Rodolfo Figari; Alessandro Teta (Annales Poincare Phys.Theor.69:413-424,1998, 1998)

On the Dirichlet problem for vectorial Hamilton-Jacobi equations - Sandro Zagatti (SIAM J. Math. Anal. 29 (1998) 1481-1491, 1998)
We give sufficient conditions for the existence of solutions to the Hamilton--Jacobi equations with Dirichlet boundary condition: $$ \\\\cases{ g(x,{\\\\hbox{\\\\rm det}}Du(x))=0, \\\\ & for a.e. $x\\\\in\\\\Omega,$\\\\cr u(x)=\\\\varphi(x), & for $x\\\\in\\\\partial\\\\Omega,$} $$ obtaining, in addition, an application to the theory of existence of minimizers for a class of nonconvex variational problems.

Error bounds for a deterministic version of the Glimm scheme - Andrea Marson; Alberto Bressan (Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176, 1998)
Consider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let $u$ be the unique viscosity solution with initial condition $u(0,x)=\\\\bar u(x)$ and let $u^\\\\varepsilon$ be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\\\\Delta x,\\\\Delta t=O(\\\\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$

Extended affine Weyl groups and Frobenius manifolds - Boris Dubrovin; Youjin Zhang (Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219, 1998)

Generation of primordial fluctuations in curved spaces - Schaeffer, Richard; Moschella, Ugo; Marco Bertola; Gorini, Vittorio (Gravit. Cosmol., 1998)

A generic classification of time-optimal planar stabilizing feedbacks - Alberto Bressan; Benedetto Piccoli (SIAM J. Control Optim. 36 (1998) 12-32, 1998)
Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto.

Geometric control approach to synthesis theory - Ugo Boscain; Benedetto Piccoli (Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001), 1998)

Geometry and analytic theory of Frobenius manifolds - Boris Dubrovin (Proceedings of the International Congress of Mathematicians : Berlin 1998, August 18 - 27. II, Invited lectures. - Bielefeld : Universität Bielefeld, Fakultät für Mathematik cop. 1998. - pages : 315-326, 1998)
Main mathematical applications of Frobenius manifolds are\\r\\nin the theory of Gromov - Witten invariants, in singularity theory, in\\r\\ndifferential geometry of the orbit spaces of reflection groups and of their\\r\\nextensions, in the hamiltonian theory of integrable hierarchies. The theory\\r\\nof Frobenius manifolds establishes remarkable relationships between\\r\\nthese, sometimes rather distant, mathematical theories.

Infinite time regular synthesis - Benedetto Piccoli (ESAIM: COCV 3 (1998) 381-405, 1998)
In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function.

Limits of variational problems for Dirichlet forms in varying domains - Gianni Dal Maso; Virginia De Cicco; Lino Notarantonio; Nicoletta A. Tchou (Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116, 1998)

Mirror Symmetry on K3 Surfaces as a Hyper-Kähler Rotation - Ugo Bruzzo; Guido Sanguinetti (Lett. Math. Phys. 45 (1998) 295-301, 1998)
We show that under the hypotheses of Strominger, Yau and Zaslow\\\'s paper, a mirror partner of a K3 surface $X$ with a fibration in special Lagrangian tori can be obtained by rotating the complex structure of $X$ within its hyperk\\\\\\\"ahler family of complex structures. The same hypotheses force the B-field to vanish.

Special functions with bounded variation and with weakly differentiable traces on the jump set - Luigi Ambrosio; Andrea Braides; Adriana Garroni (NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243, 1998)

Uniqueness for discontinuous ODE and conservation laws - Alberto Bressan; Wen Shen (Nonlinear Analysis 34 (1998) 637-652, 1998)
Consider a scalar O.D.E. of the form $\\\\dot x=f(t,x),$ where $f$ is possibly discontinuous w.r.t. both variables $t,x$. Under suitable assumptions, we prove that the corresponding Cauchy problem admits a unique solution, which depends H\\\\\\\"older continuously on the initial data.\\nOur result applies in particular to the case where $f$ can be written in the form $f(t,x)\\\\doteq g\\\\big( u(t,x)\\\\big)$, for some function $g$ and some solution $u$ of a scalar conservation law, say $u_t+F(u)_x=0$. In turn, this yields the uniqueness and continuous dependence of solutions to a class of $2\\\\times 2$ strictly hyperbolic systems, with initial data in $\\\\L^\\\\infty$.

Capacity theory for monotone operators - Gianni Dal Maso; Igor V. Skrypnik (Potential Anal. 7 (1997), no. 4, 765-803, 1997)
If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$.

Comportamento asintotico delle soluzioni di problemi di Dirichlet - Gianni Dal Maso (Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277, 1997)

On Existence and Continuous Dependence for Systems of Conservation Laws - Paolo Baiti (SISSA, 1997)
Keywords: Conservation laws

Flat pencils of metrics and Frobenius manifolds - Boris Dubrovin (Integrable systems and algebraic geometry : proceedings of the Taniguchi symposium 1997, Kobe, June 30 - July 4, 1997 and Research Institute for Mathematical Sciences, Kyoto University, July 7 - 11, 1997 / eds. M.-H. Saito, Y. Shimizu and K. Ueno. - Sing, 1997)
This paper is based on the author\\\'s talk at 1997 Taniguchi Symposium \\\"Integrable Systems and Algebraic Geometry\\\". We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics. It is shown that, under certain homogeneity assumptions, these two objects are identical. The flat pencils of contravariant metrics on a manifold $M$ appear naturally in the classification of bihamiltonian structures of hydrodynamics type on the loop space $L(M)$. This elucidates the relations between Frobenius manifolds and integrable hierarchies.

Functionals of the Peierls - Fröhlich Type and the Variational Principle for the Whitham Equations - Boris Dubrovin (Solitons, geometry, and topology : on the crossroad / V. M. Buchstaber, S. P. Novikov editors.- Providence : American Mathematical Society, 1997. - ( American mathematical society translations. Series 2. - vol. 179). - pages : 35-44, 1997)

Homogeneous tangent vectors and high order necessary conditions for optimal controls - Fabio Ancona (J. Dynam. Control Systems 3 (1997), no. 2, 205--240, 1997)

Kam theorem for generic analytic perturbations of the Guler system - Marta Mazzocco (Z. Angew. Math. Phys. 48 (1997), no. 2, 193-219, 1997)
We apply here KAM theory to the fast rotations of a rigid body with a fixed point, subject to a purely positional potential. The problem is equivalent to a small perturbation of the Euler system. The difficulty is that the unperturbed system is properly degenerate, namely the unperturbed Hamiltonian depends only on two actions. Following the scheme used by Arnol\\\'d for the N-body problem, we use part of the perturbation to remove the degeneracy: precisely, we construct Birkhoff normal form up to a suitable finite order, thus eliminating the two fast angles; the resulting system is nearly integrable and (generically) no more degenerate, so KAM theorem applies. The resulting description of the motion is that, if the initial kinetic energy is sufficiently large, then for most initial data the angular momentum has nearly constant module, and moves slowly in the space, practically following the level curves of the initial potential averaged on the two fast angles; on the same time the body precesses around the instantaneous direction of the angular momentum, essentially as in the Euler-Poinsot motion. We also provide two simple physical examples, where the procedure does apply.

Krichever maps, Faà di Bruno polynomials, and cohomology in KP theory - Gregorio Falqui; Cesare Reina; Alessandro Zampa (Lett. Math. Phys. 42 (1997) 349-361, 1997)
We study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.

The semigroup generated by a temple class system with large data - Paolo Baiti; Alberto Bressan (Differential Integral Equations 10 (1997), no. 3, 401-418, 1997)
We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation.

Shift-differentiability of the flow generated by a conservation law - Alberto Bressan; Graziano Guerra (Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58., 1997)
The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition.

Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains - Rodica Toader (SISSA, 1997)
Keywords: Dirichlet problems

Some properties of reachable solutions of nonlinear elliptic equations with measure data - Gianni Dal Maso; Annalisa Malusa (Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396, 1997)

Statistics in space dimension two - Gianfausto Dell'Antonio; Rodolfo Figari; Alessandro Teta (Lett. Math. Phys. 40 (1997), no. 3, 235-256, 1997)
We construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect).

Structural stability for time-optimal planar sytheses - Alberto Bressan; Benedetto Piccoli (Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371, 1997)

Three-Phase Solutions of the Kadomtsev - Petviashvili Equation - Boris Dubrovin; Ron Flickinger; Harvey Segur (Studies in Applied Mathematics. Year : 1997 ; Volume: 99 ; Issue: 2 ; Pages: 137-203, 1997)
The Kadomtsev]Petviashvili KP. equation is known to admit explicit periodic\\r\\nand quasiperiodic solutions with N independent phases, for any integer\\r\\nN, based on a Riemann theta-function of N variables. For Ns1 and 2,\\r\\nthese solutions have been used successfully in physical applications. This\\r\\narticle addresses mathematical problems that arise in the computation of\\r\\ntheta-functions of three variables and with the corresponding solutions of\\r\\nthe KP equation. We identify a set of parameters and their corresponding\\r\\nranges, such that e¨ery real-valued, smooth KP solution associated with a\\r\\nRiemann theta-function of three variables corresponds to exactly one choice\\r\\nof these parameters in the proper range. Our results are embodied in a\\r\\nprogram that computes these solutions efficiently and that is available to the\\r\\nreader. We also discuss some properties of three-phase solutions.

Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws - Graziano Crasta; Benedetto Piccoli (Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5, 1997)

A capacity method for the study of Dirichlet problems for elliptic systems in varying domains - Gianni Dal Maso; Rodica Toader (Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277, 1996)

The semigroup approach to systems of conservation laws - Alberto Bressan (Mat. Contemp. 10 (1996) 21-74, 1996)

Solving Honig generic problem about Volterra integral equations - Giovanni Vidossich (Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498, 1996)

Capacity and Dirichlet problems in varying domains - Gianni Dal Maso (SISSA Library, 1995)

Classical solutions for a perturbed N-body system - Gianfausto Dell'Antonio (Topological nonlinear analysis, II (Frascati, 1995), 1--86, Progr. Nonlinear Differential Equations Appl., 27, Birkhauser Boston, Boston, MA, 1997, 1995)

An existence result in a problem of the vectorial case of the calculus of variations - Arrigo Cellina; Sandro Zagatti (SIAM, 1995)
SIAM J. Control Optim. 33 (1995) 960-970

Geometry of 2D topological field theories - Boris Dubrovin (Integrable systems and quantum groups : lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1995 / R. Donagi, B. Dubrovin, E. Frenkel... [et al.] ; editors, M. Francavig, 1995)
These notes are devoted to the theory of “equations of associativity”\\r\\ndescribing geometry of moduli spaces of 2D topological field theories.

Quantum homogeneous spaces at roots of unity - Cesare Reina; Alessandro Zampa (Quantization, Coherent States and Poisson Structures, Proc. XIVth Workshop on Geometric Methods in Physics, Bialowieza, Poland, 9-15 July 1995, eds. A. Strasburger,\\nS.T. Ali, J.-P. Antoine, J.-P. Gazeau , A. Odzijewicz, Polish Scientific Publisher PWN 1, 1995)

Some control problems for the pendulum - Benedetto Piccoli (Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318, 1995)
The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems.

Special functions of bounded deformation - Giovanni Bellettini; Alessandra Coscia; Gianni Dal Maso (SISSA Library, 1995)

Unique solutions of 2x2 conservation laws with large data - Alberto Bressan; Rinaldo M. Colombo (Indiana Univ. Math. J. 44 (1995), no. 3, 677-725, 1995)
For a 2x2 hyperbolic system of conservation laws, we first consider a Riemann problem with arbitrarily large data. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. We then establish a uniqueness result for large BV solutions, valid within the same class of functions where a local existence theorem can be proved.

Algebraic-geometrical Darboux coordinates in R-matrix formalism - P. Diener; Boris Dubrovin (SISSA, 1994)

Analysis of Singularity Structures for Quasi-Integrable Hamiltonian Systems - Simonetta Abenda (SISSA, 1994)
Keywords: Hamiltonian systems

Asymptotic Behaviour of Dirichlet Problems in Perforated Domains - Adriana Garroni (SISSA, 1994)
Keywords: Dirichlet problems

Hilbert schemes of points on some K3 surfaces and Gieseker stable boundles - Ugo Bruzzo; Antony Maciocia (MATH PROC CAMBRIDGE 120: 255-261 Part 2, 1994)
By using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces $X$ the punctual Hilbert schemes $\\\\Hilb^n(X)$ can be identified, for all $n\\\\geq 1$, with moduli spaces of Gieseker stable vector bundles on $X$ of rank $1+2n$. We also introduce a new Fourier-Mukai type transform for such surfaces.

Integrable functional equations and algebraic geometry - Boris Dubrovin; A.S. Fokas; P.M. Santini (Duke Mathematical Journal. Volume: 76, Issue: 2, Pages: 645-668, 1994)

Limits of Dirichlet problems in perforated domains: a new formulation - Gianni Dal Maso; Rodica Toader (Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360, 1994)

A version of Olech\\\'s lemma in a problem of the calculus of variations - Arrigo Cellina; Sandro Zagatti (SIAM J. Control Optim. 32 (1994) 1114-1127, 1994)
This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data.

A Borel-Weil-Bott approach to representations of \rm sl\sb q(2,C) - Davide Franco; Cesare Reina (Lett. Math. Phys. 29 (1993) 215-217, 1993)
We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.

Dispersion relations for non-linear waves and the Schottky problem - Boris Dubrovin (Important developments in soliton theory / A. S. Fokas, V. E. Zakharov (eds.) - Berlin : Springer-Verlag, 1993. - pages : 86-98, 1993)
An approach to the Schottky problem of specification of periods of holomorphic differentials\\r\\non Riemann surfaces (or, equivalently, specification of Jacobians among all principaly\\r\\npolarized Abelian varieties) based on the theory of Kadomtsev - Petviashvili equation,\\r\\nis discussed.

Geometry and integrability of topological-antitopological fusion - Boris Dubrovin (Communications in Mathematical Physics. Volume 152, Issue 3, March 1993, Pages 539-564, 1993)
Integrability of equations of topological-antitopological fusion (being proposed\\r\\nby Cecotti and Vafa) describing the ground state metric on a given 2D topological\\r\\nfield theory (TFT) model, is proved. For massive TFT models these equations\\r\\nare reduced to a universal form (being independent on the given TFT model) by\\r\\ngauge transformations. For massive perturbations of topological conformal field theory\\r\\nmodels the separatrix solutions of the equations bounded at infinity are found\\r\\nby the isomonodromy deformations method. Also it is shown that the ground state\\r\\nmetric together with some part of the underlined TFT structure can be parametrized\\r\\nby pluriharmonic maps of the coupling space to the symmetric space of real positive\\r\\ndefinite quadratic forms.

Integrable systems and classification of 2D topological field theories - Boris Dubrovin (Integrable systems : the Verdier memorial conference : actes du colloque international de Luminy / Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach editors. - Boston [etc.] : Birkhauser, c1993. - p. 313-359, 1993)
In this paper we consider from the point of view of differential geometry and of the\\r\\ntheory of integrable systems the so-called WDVV equations as defining relations of 2-\\r\\ndimensional topological field theory. A complete classification of massive topological conformal\\r\\nfield theories (TCFT) is obtained in terms of monodromy data of an auxillary\\r\\nlinear operator with rational coefficients. Procedure of coupling of a TCFT to topological\\r\\ngravity is described (at tree level) via certain integrable bihamiltonian hierarchies of\\r\\nhydrodynamic type and their τ -functions. A possible role of bihamiltonian formalism in\\r\\ncalculation of high genus corrections is discussed. As a biproduct of this discussion new\\r\\nexamples of infinite dimensional Virasoro-type Lie algebras and their nonlinear analogues\\r\\nare constructed. As an algebro-geometrical applications it is shown that WDVV is just the\\r\\nuniversal system of integrable differential equations (high order analogue of the Painlev´e-\\r\\nVI) specifying periods of Abelian differentials on Riemann surfaces as functions on moduli\\r\\nof these surfaces.

Topological conformal field theory from the point of view of integrable systems - Boris Dubrovin (Integrable quantum field theories / edited by L. Bonora ... \et al.! - New York : Plenum Press, 1993. - page : 283 - 302., 1993)
Recent results on classification of massive topological conformal field theories (TCFT) in terms of monodromy data of auxiliary linear operators with rational coefficients are presented. Procedure of coupling of a TCFT to topological gravity is described (at tree-level approximation) via certain integrable hierarchies of hydrodynamic type and their tau-functions. It is explained how the calculation of the ground state metric on TCFT can be interpreted in terms of harmonic maps. Also a construction of some models via Coxeter groups is described.

Workshop on point interactions, Trieste, 21-23 December 1992 - Gianfausto Dell'Antonio (SISSA Library, 1993)

Hamiltonian formalism of Whitham-type hierarchies and topological Landau - Ginsburg models - Boris Dubrovin (Communications in Mathematical Physics. Volume 145, Issue 1, March 1992, Pages 195-207, 1992)
We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii\\r\\nhierarchy is involved in the Landau-Ginsburg topological models (for An-Series):\\r\\nthe Casimirs for the first P.B. give the correct coupling parameters for the perturbed\\r\\ntopological minimal model; the correspondence {coupling parameters} ~ {primary\\r\\nfields} is determined by the second P.B. The partition function (at the tree level) and\\r\\nthe chiral algebra for LG models are calculated for any genus g.

Integrable systems in topological field theory - Boris Dubrovin (Nuclear Physics B. Volume 379, Issue 3, 1992, pages : 627-689, 1992)
Integrability of the system of PDE for dependence on coupling parameters of the (tree-level) primary partition function in massive topological field theories, being imposed by the associativity of the perturbed primary chiral algebra, is proved. In the conformal case it is shown that all the topological field theories are classified as solutions of a universal high-order Painlevé-type equation. Another integrable hierarchy (of systems of hydrodynamic type) is shown to describe coupling to gravity of the matter sector of any topological field theory. Different multicritical models with the given structure of primary correlators are identified with particular self-similar solutions of the hierarchy. The partition function of any of the models is calculated as the corresponding tau-function of the hierarchy.

Some Problems in the Calculus of the Variations - Sandro Zagatti (SISSA, 1992)
Keywords: Calculus of variations

Topological "observables" in semiclassical field theories - Margherita Nolasco; Cesare Reina (Phys. Lett. B 297 (1992) 82-88, 1992)
We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $σ$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}} → \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $dμ$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_φ$ in the background of an instanton $φ \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, dμ$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

A variational method in image segmentation: existence and approximation result - Gianni Dal Maso; Jean-Michel Morel; Sergio Solimini (Acta Math. 168 (1992), no.1-2, p. 89-151, 1992)

A class of absolute retracts of dwarf spheroidal galaxies - Alberto Bressan; Arrigo Cellina; Andrzej Fryszkowski (Proc.Amer.Math.Soc. 112 (1991), no.2, 413, 1991)

Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory - Boris Dubrovin (Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238., 1991)
We construct flat Riemannian metrics on moduli spaces of algebraic curves with marked meromorphic function. This gives a new class of exact algebraic-geometry solutions to certain non-linear equations in terms of functions on the moduli spaces. We show that the Riemannian metrics on the moduli spaces coincide with two-point correlators in topological conformal field theory and calculate the partition function for A_n model for arbitrary genus. A universal method for constructing complete families of conservation laws for Whitham-type hierarchies of PDEs is also proposed.

Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions - Giuseppe Buttazzo; Gianni Dal Maso (Appl.Math.Optim. 23 (1991), no.1, p. 17-49., 1991)

On systems of ordinary differential equations with measures as controls - Gianni Dal Maso; Franco Rampazzo (Differential Integral Equations 4 (1991), no.4, p.739-765., 1991)

Algebraic differential calculus for gauge theories - Giovanni Landi; Giuseppe Marmo (Nuclear Phys. B. Proc. Suppl. 18A (1990), 171, 1990)

Chern-Simons forms on principal superfiber bundles - Giovanni Landi; Claudio Bartocci; Ugo Bruzzo (J.Math.Phys.31:45,1990, 1990)
A graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a ``superextension\\\'\\\' of the Dirac monopole is discussed.

Correctors for the homogeneization of monotone operators - Gianni Dal Maso; Anneliese Defranceschi (Differential Integral Equations 3 (1990), no.6, p.1151-1166., 1990)

Existence and continuous dependence for discontinuous O.D.E.s - Alberto Bressan; Giovanni Colombo (Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311, 1990)

Existence of solutions for a class of non-convex differential inclusions - Fabio Ancona; Giovanni Colombo (Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76, 1990)

G-convergence of monotone operators - Valeria Chiadò Piat; Gianni Dal Maso; Anneliese Defranceschi (Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160, 1990)

A general chain rule for distributional derivatives - Luigi Ambrosio; Gianni Dal Maso (Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702, 1990)

A general existence theorem for boundary value problems for ordinary differential equations - Giovanni Vidossich (Nonlinear Anal. 15 (1990), no. 10, 897--914, 1990)

Moduli Spaces and Geometrical Aspects of Two-Dimensional Conformal Field Theories - Gregorio Falqui (SISSA, 1990)
Keywords: Algebraic curves

N=2 super Riemann surfaces and algebraic geometry - Cesare Reina; Gregorio Falqui (J. Math. Phys. 31 (1990), no.4, 948-952, 1990)
The geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems.

A note on the global structure of supermoduli spaces - Cesare Reina; Gregorio Falqui (Comm.Math.Phys. 31 (1990), no.4, 948, 1990)

Quadratic forms for singular perturbations of the Laplacian - Alessandro Teta (Publ. Res. Inst. Math. Sci. 26 (1990), no. 5, 803--817, 1990)

Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions - Giuseppe Buttazzo; Gianni Dal Maso (Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535., 1990)

An approach to the thin obstacle problem for variational functionals depending on vector - Gianni Dal Maso; Roberta Musina (Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743., 1989)

On the continuous dependence of solutions of boundary value problems for ordinary differential equations (Revised version) - Giovanni Vidossich (J. Differential Equations 82 (1989), no. 1, 1-14, 1989)

On the continuous dependence of solutions of boundary value problems for ordinary differential equations - Giovanni Vidossich (J. Differential Equations 82 (1989), no. 1, 1--14, 1989)

Convergence of unilateral problems for monotone operators - Gianni Dal Maso; Anneliese Defranceschi (J. Analyse Math. 53 (1989), 269--289, 1989)

Hyperbolic equations as ordinary differential equations in Banach spaces - Giovanni Vidossich (SISSA Library, 1989)

Limits of obstacle problems for the area functional. - Gianni Dal Maso; G. Carere; Antonio Leaci; Eduardo Pascali (Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309, 1989)

On the number of families of periodic solutions of a Hamiltonian system near equilibrium. II. (English. Italian summary) - Gianfausto Dell'Antonio; Biancamaria D'Onofrio (Boll. Un. Mat. Ital. B (7) 3 (1989), no. 3, 579-590, 1989)

A pointwise regularity theory for the two-obstacle problem - Gianni Dal Maso; Umberto Mosco; Maria Agostina Vivaldi (Acta Math. 163 (1989), no. 1-2, 57-107, 1989)

Singular perturbation of the Laplacian and connections with models of random media - Alessandro Teta (SISSA, 1989)

On the solvability of boundary value problems for higher order ordinary differential equations (Revised version) - Giovanni Vidossich (Nonlinear Anal. 13 (1989), no. 10, 1171-1179, 1989)

On the solvability of boundary value problems for higher order ordinary differential equations - Giovanni Vidossich (Nonlinear Anal. 13 (1989), no. 10, 1171-179, 1989)

Surfaces of minimal area enclosing a given body in R\\\\sp 3. - Giovanni Mancini; Roberta Musina (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990)., 1989)

Upper semicontinuous differential inclusions without convexity - Alberto Bressan; Arrigo Cellina; Giovanni Colombo (Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775, 1989)

Algebraic reduction of the \\\'t Hooft-Polyakov monopole to the Dirac monopole. - Giovanni Landi; Giuseppe Marmo (Phys. Lett. B 201 (1988), no. 1, 101-104., 1988)

An Algebraic Setting for Gauge Theories - Giovanni Landi (SISSA, 1988)

On differential systems with vector-valued impulsive controls. - Alberto Bressan; Franco Rampazzo (Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656, 1988)

Einstein algebras and the algebraic Kaluza-Klein monopole. - Giovanni Landi; Giuseppe Marmo (Phys. Lett. B 210 (1988), no. 1-2, 68--72., 1988)

Generalized Baire category and differential inclusions in Banach spaces. - Alberto Bressan; Giovanni Colombo (J. Differential Equations 76 (1988), no. 1, 135-158., 1988)

Holes and obstacles - Roberta Musina; Giovanni Mancini (Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988), no. 4, 323-345, 1988)

H-surfaces with obstacles. (Italian) - Roberta Musina (Ann. Univ. Ferrara Sez. VII (N.S.) 34 (1988), 1-14, 1988)

A Kellogg property for µ-capacities - Gianni Dal Maso; Anneliese Defranceschi (Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135, 1988)

Limits of nonlinear Dirichlet problems in varying domains. - Gianni Dal Maso; Anneliese Defranceschi (Manuscripta Math. 61 (1988), no. 3, 251-278., 1988)
We study the general form of the limit, in the sense of gamma-convergence, of a sequence of nonlinear variational problems in varying domains with Dirichlet boudary conditions. The asymptotic problem is characterized in terms of the limit of suitable nonlinear capacities associated to the domains.

Methods of stochastic stability and properties of the Gribov horizon in the stochastic quantization of gauge theories - Gianfausto Dell'Antonio (Stochastic processes, physics and geompetry (Ascona and Locarno, 1988), 302, World Sci.Publishing,NJ(1990), 1988)

Some properties of a class of nonlinear variational $m$-capacities - Gianni Dal Maso; Anneliese Defranceschi (J.Funct.Anal. 79, 1988, no. 2, 476-492, 1988)

Susy-curves and supermoduli - Gregorio Falqui; Cesare Reina (SISSA Library, 1988)

Variational inequalities for the biharmonic operator with variable obstacles. - Gianni Dal Maso; Gabriella Paderni (Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989), 1988)

Variational Problems with Obstructions - Roberta Musina (SISSA, 1988)

Extensions of Lie superalgebras and supersymmetric Abelian gauge fields. - Giovanni Landi; Giuseppe Marmo (Phys. Lett. B 193 (1987), no. 1, 61-66., 1987)

Graded Chern-Simons terms - Giovanni Landi; Giuseppe Marmo (Phys. Lett. B 192 (1987), no. 1-2, 81-88., 1987)

Integral representation of some convex local functionals. - Gianni Dal Maso; Gabriella Paderni (Ricerche Mat. 36 (1987), no. 2, 197-214, 1987)

Lie algebra extensions and abelian monopoles. - Giovanni Landi; Giuseppe Marmo (Phys. Lett. B 195 (1987), no. 3, 429-434, 1987)

Limits of nonlinear Dirichlet problems in varying domains. (Italian) - Gianni Dal Maso; Anneliese Defranceschi (Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118, 1987)

Solutions with minimal period for Hamiltonian systems in a potential well. - Antonio Ambrosetti; Vittorio Coti Zelati (Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296, 1987)

Symmetry breaking in Hamiltonian systems - Antonio Ambrosetti; Vittorio Coti Zelati; Ivar Ekeland (J. Differential Equations 67 (1987), no. 2, 165-184, 1987)

Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984) - Gianni Dal Maso (Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190, 1986)

Dirichlet problems for demicoercive functionals - Gabriele Anzellotti; Giuseppe Buttazzo; Gianni Dal Maso (Nonlinear anal. 10(1986), no.6, 603-613, 1986)

The natural spinor connection on $S\\\\sb 8$ is a gauge field - Giovanni Landi (Lett. Math. Phys. 11 (1986), no. 2, 171-175, 1986)

Flat connections for Lax hierarchies on coadjoint orbits - Giovanni Landi; Sergio De Filippo (Phys. Lett. A 108 (1985), no. 7, 311-314, 1985)

Maximal acceleration and Sakharov's limiting temperature - Eduardo R. Caianiello; Giovanni Landi (Lett. Nuovo Cim. 42 (1985) 70-72, 1985)
It is shown that Sakharov's maximal temperature, derived by him from astrophysical considerations, is a straightforward consequence of the maximal acceleration introduced by us in previous works.

Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets - Gianni Dal Maso (J. Funct. Anal. 62 (1985), no. 2, 119--159, 1985)

Some singular perturbation problems in the calculus of variations. - Gianni Dal Maso (Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985, 1985)

The two-point boundary value problem from the Cauchy problem - Giovanni Vidossich (J. Differential Equations 60 (1985), no. 1, 1--20, 1985)

Weak convergence of measures on spaces of semicontinuous functions. - Gianni Dal Maso; Ennio De Giorgi; Luciano Modica (Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106, 1985)

Spin Structures and Global Conformal Transformations - Ludwik Dabrowski (SISSA, 1984)
Keywords: Spinors

On the asymptotic behaviour of solutions to Pazy\\\'s class of evolution equations - Giovanni Vidossich (SISSA Library, 1983)

Towards a theory for periodic solutions to first order ordinary differential equations. - Giovanni Vidossich (SISSA Library, 1983)

A criterion for he existence of maximal solutions of strongly nonlinear elliptic problems - Giovanni Vidossich (SISSA Library, 1982)

Differential equations with multiple solutions and nonlinear functional analysis - Antonio Ambrosetti (Equadiff 82 (Wurzburg, 1982), 10--37, Lecture Notes in Math., 1017, Springer, Berlin, 1983, 1982)

On the obstacle problem for strongly nonlinear elliptic equations - Giovanni Vidossich (SISSA Library, 1982)

Three uniqueness theorems for strongly non-linear elliptic problems - Giovanni Vidossich (SISSA Library, 1982)

Recent advances in the study of the existence of periodic orbits of Hamiltonian systems - Antonio Ambrosetti (Advances in Hamiltonian systems (Rome, 1981), 1--22, Ann. CEREMADE, Birkhauser Boston, Boston, MA, 1983., 1981)

Uniqueness and multiplicity of periodic solutions to first order ordinary differential equations - Giovanni Vidossich (Not Found)