@article {2022, title = {Long-time stability of the quantum hydrodynamic system on irrational tori}, journal = {Mathematics in Engineering}, volume = {4}, year = {2022}, pages = {1-24}, keywords = {Euler-Korteweg, irrational tori, long time stability, QHD system, Small divisors}, issn = {2640-3501}, doi = {10.3934/mine.2022023}, url = {https://www.aimspress.com/article/doi/10.3934/mine.2022023}, author = {Roberto Feola and Felice Iandoli and Federico Murgante} } @unpublished {romor2021las, title = {A local approach to parameter space reduction for regression and classification tasks}, year = {2021}, note = {Submitted}, author = {Francesco Romor and Marco Tezzele and Gianluigi Rozza} } @article {2021, title = {Local Well Posedness of the Euler{\textendash}Korteweg Equations on $${{\mathbb {T}}^d}$$}, volume = {33}, year = {2021}, month = {2021/09/01}, pages = {1475 - 1513}, abstract = {

We consider the Euler{\textendash}Korteweg system with space periodic boundary conditions $$ x \in {\mathbb {T}}^d$$. We prove a local in time existence result of classical solutions for irrotational velocity fields requiring natural minimal regularity assumptions on the initial data.

}, isbn = {1572-9222}, url = {https://doi.org/10.1007/s10884-020-09927-3}, author = {Massimiliano Berti and Alberto Maspero and Federico Murgante} } @article {FEOLA2019119, title = {Local well-posedness for quasi-linear NLS with large Cauchy data on the circle}, journal = {Annales de l{\textquoteright}Institut Henri Poincar{\'e} C, Analyse non lin{\'e}aire}, volume = {36}, number = {1}, year = {2019}, pages = {119 - 164}, abstract = {

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schr{\"o}dinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

}, keywords = {Dispersive equations, Energy method, Local wellposedness, NLS, Para-differential calculus, Quasi-linear PDEs}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2018.04.003}, url = {http://www.sciencedirect.com/science/article/pii/S0294144918300428}, author = {Roberto Feola and Felice Iandoli} } @article {2019, title = {A localized reduced-order modeling approach for PDEs with bifurcating solutions}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {351}, year = {2019}, pages = {379-403}, abstract = {

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. Although ROMs have been successfully used in many settings, ROMs built specifically for the efficient treatment of PDEs having solutions that bifurcate as the values of input parameters change have not received much attention. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does not respect the often large differences in the PDE solutions corresponding to different subregions. In this work, we develop and test a new ROM approach specifically aimed at bifurcation problems. In the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

}, doi = {10.1016/j.cma.2019.03.050}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85064313505\&doi=10.1016\%2fj.cma.2019.03.050\&partnerID=40\&md5=8b095034b9e539995facc7ce7bafa9e9}, author = {Martin W. Hess and Alla, Alessandro and Annalisa Quaini and Gianluigi Rozza and Max Gunzburger} } @article {2019, title = {A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {351}, year = {2019}, pages = {379-403}, abstract = {

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. In this work, a ROM is developed and tested for the treatment of nonlinear PDEs whose solutions bifurcate as input parameter values change. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does no respect not take advantage of the often large differences in the PDE solutions corresponding to different subregions. Instead, in the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

}, doi = {10.1016/j.cma.2019.03.050}, url = {https://arxiv.org/abs/1807.08851}, author = {Martin W. Hess and Alla, Alessandro and Annalisa Quaini and Gianluigi Rozza and Max Gunzburger} } @article {2018, title = {Local moduli of semisimple Frobenius coalescent structures}, number = {arXiv;1712.08575}, year = {2018}, institution = {SISSA}, abstract = {

There is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.

}, url = {http://preprints.sissa.it/handle/1963/35304}, author = {Giordano Cotti and Boris Dubrovin and Davide Guzzetti} } @article {1806.03437, title = {Long time existence for fully nonlinear NLS with small Cauchy data on the circle}, year = {2018}, author = {Feola Roberto and Felice Iandoli} } @article {Dell{\textquoteright}Antonio2018, title = {Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction}, journal = {Annales Henri Poincar{\'e}}, volume = {19}, number = {1}, year = {2018}, month = {Jan}, pages = {283{\textendash}322}, abstract = {

We prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schr{\"o}dinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1\<p\<3 and unbounded otherwise.

}, issn = {1424-0661}, doi = {10.1007/s00023-017-0628-4}, url = {https://doi.org/10.1007/s00023-017-0628-4}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli and Raffaele Scandone and Kenji Yajima} } @article {2017, title = {A Lagrangian approach for scalar multi-d conservation laws}, number = {SISSA;36/2017/MATE}, year = {2017}, url = {http://preprints.sissa.it/handle/1963/35290}, author = {Stefano Bianchini and Paolo Bonicatto and Elio Marconi} } @article {bianchini2017lagrangian, title = {Lagrangian representations for linear and nonlinear transport}, journal = {Contemporary Mathematics. Fundamental Directions}, volume = {63}, number = {3}, year = {2017}, pages = {418{\textendash}436}, publisher = {Peoples{\textquoteright} Friendship University of Russia}, abstract = {

In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

}, doi = {10.22363/2413-3639-2017-63-3-418-436}, url = {http://www.mathnet.ru/php/archive.phtml?wshow=paper\&jrnid=cmfd\&paperid=327\&option_lang=eng}, author = {Stefano Bianchini and Paolo Bonicatto and Elio Marconi} } @article { refId0, title = {Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish}, journal = {ESAIM: COCV}, volume = {23}, number = {2}, year = {2017}, pages = {593-625}, abstract = {

We introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a {\textquotedblleft}local{\textquotedblright} quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101{\textendash}126], where no viscosity in the adhesive is taken into account.

}, doi = {10.1051/cocv/2016006}, url = {https://doi.org/10.1051/cocv/2016006}, author = {Riccardo Scala} } @article {2017, title = {Linear Hyperbolic Systems in Domains with Growing Cracks}, volume = {85}, year = {2017}, month = {2017/06/01}, pages = {149 - 185}, abstract = {

We consider the hyperbolic system {\"u}$${ - {\rm div} (\mathbb{A} \nabla u) = f}$$in the time varying cracked domain $${\Omega \backslash \Gamma_t}$$, where the set $${\Omega \subset \mathbb{R}^d}$$is open, bounded, and with Lipschitz boundary, the cracks $${\Gamma_t, t \in [0, T]}$$, are closed subsets of $${\bar{\Omega}}$$, increasing with respect to inclusion, and $${u(t) : \Omega \backslash \Gamma_t \rightarrow \mathbb{R}^d}$$for every $${t \in [0, T]}$$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system v̈$${ - {\rm div} (\mathbb{B}\nabla v) + a\nabla v - 2 \nabla \dot{v}b = g}$$on the fixed domain $${\Omega \backslash \Gamma_0}$$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions v, which allows us to prove a continuous dependence result for both systems. The same study has already been carried out in [3, 7] in the scalar case.

}, isbn = {1424-9294}, url = {https://doi.org/10.1007/s00032-017-0268-7}, author = {Maicol Caponi} } @article {2017, title = {Linearisation of multiwell energies}, number = {SISSA;31/2017/MATE}, year = {2017}, abstract = {Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours.}, url = {http://preprints.sissa.it/handle/1963/35288}, author = {Roberto Alicandro and Gianni Dal Maso and Giuliano Lazzaroni and Mariapia Palombaro} } @article {dal2017lower, title = {Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation}, journal = {Advances in Calculus of Variations}, volume = {10}, number = {2}, year = {2017}, pages = {183{\textendash}207}, publisher = {De Gruyter}, abstract = {

We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

}, doi = {10.1515/acv-2015-0036}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @article {2015, title = {A lower semicontinuity result for a free discontinuity functional with a boundary term}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, volume = {108}, year = {2017}, pages = {952-990}, chapter = {952}, abstract = {

We study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

}, doi = {10.1016/j.matpur.2017.05.018}, url = {http://hdl.handle.net/20.500.11767/15979}, author = {Stefano Almi and Gianni Dal Maso and Rodica Toader} } @article {2016, title = {Large KAM tori for perturbations of the dNLS equation}, number = {arXiv;1603.09252}, year = {2016}, abstract = {We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2{\texttimes}2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues.}, url = {http://preprints.sissa.it/handle/1963/35284}, author = {Massimiliano Berti and Thomas Kappeler and Riccardo Montalto} } @article {20.500.11767_11950, title = {LinearOperator {\textendash} a generic, high-level expression syntax for linear algebra}, journal = {COMPUTERS \& MATHEMATICS WITH APPLICATIONS}, volume = {72}, year = {2016}, pages = {1{\textendash}24}, doi = {10.1016/j.camwa.2016.04.024}, author = {Matthias Maier and Mauro Bardelloni and Luca Heltai} } @article {DESIMONE2015254, title = {Liquid crystal elastomer strips as soft crawlers}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {84}, year = {2015}, pages = {254 - 272}, abstract = {

In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, {\textquoteleft}breathing-like{\textquoteright} deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

}, keywords = {Crawling motility, Directional surfaces, Frictional interactions, Liquid crystal elastomers, Soft biomimetic robots}, issn = {0022-5096}, doi = {https://doi.org/10.1016/j.jmps.2015.07.017}, url = {http://www.sciencedirect.com/science/article/pii/S0022509615300430}, author = {Antonio DeSimone and Paolo Gidoni and Giovanni Noselli} } @article {2014, title = {Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length}, number = {Nonlinear Differential Equations and Applications}, year = {2014}, publisher = {SISSA}, abstract = {

We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

}, keywords = {cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions}, doi = {10.1007/s00030-014-0291-0}, url = {http://hdl.handle.net/1963/7271}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @inbook {2014, title = {Lecture notes on gradient flows and optimal transport}, number = {London Mathematical Society Lecture Note Series;volume 413; pages 100-144;}, year = {2014}, note = {Book title: Optimal transportation}, publisher = {Cambridge University Press}, organization = {Cambridge University Press}, abstract = {We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.}, doi = {10.1017/CBO9781107297296}, url = {http://urania.sissa.it/xmlui/handle/1963/35093}, author = {Sara Daneri and Giuseppe Savar{\`e}} } @article {2014, title = {Legendre duality on hypersurfaces in K{\"a}hler manifolds}, number = {Advances in Geometry;volume 14; issue 2; pages 277-286;}, year = {2014}, publisher = {Walter de Gruyter and Co.}, abstract = {We give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional K{\"a}hler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.}, doi = {10.1515/advgeom-2014-0016}, url = {http://urania.sissa.it/xmlui/handle/1963/34777}, author = {Vittorio Martino} } @article {davoli_2014, title = {Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, volume = {20}, number = {3}, year = {2014}, pages = {725{\textendash}747}, publisher = {EDP Sciences}, abstract = {

The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von K{\'a}rm{\'a}n plate theory and the linearized plate theory.

}, doi = {10.1051/cocv/2013081}, author = {Elisa Davoli} } @article {2014, title = {Lipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups}, number = {Journal of geometric analysis;volume 24; issue 1; pages 169-189;}, year = {2014}, publisher = {Springer}, abstract = {In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.}, doi = {10.1007/s12220-012-9332-2}, url = {http://urania.sissa.it/xmlui/handle/1963/34699}, author = {Vittorio Martino and Annamaria Montanari} } @article {2013, title = {Local and global minimality results for a nonlocal isoperimetric problem on R^N}, journal = { SIAM Journal on Mathematical Analysis}, volume = {46}, number = {Siam journal on mathematical analysis}, year = {2014}, pages = {2310-2349}, publisher = {SIAM Publications}, abstract = {

We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

}, keywords = {Nonlocal isoperimetric problem}, doi = {10.1137/130929898}, url = {http://hdl.handle.net/1963/6984}, author = {Marco Bonacini and Riccardo Cristoferi} } @article {11062, title = {Local behavior of fractional p-minimizers}, number = {SISSA preprint;10/2014/MATE}, year = {2014}, publisher = {SISSA}, abstract = {

We extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

}, keywords = {fractional Sobolev spaces}, author = {Agnese Di Castro and Tuomo Kuusi and Giampiero Palatucci} } @article {MR3218334, title = {On local super-penalization of interior penalty discontinuous Galerkin methods}, journal = {Int. J. Numer. Anal. Model.}, volume = {11}, number = {3}, year = {2014}, pages = {478{\textendash}495}, issn = {1705-5105}, author = {Andrea Cangiani and Chapman, John and E.H. Georgoulis and Jensen, Max} } @article {2014, title = {On the Lp-differentiability of certain classes of functions}, number = {Revista Matematica Iberoamericana;Volume 30; issue 1; pp. 349-367;}, year = {2014}, publisher = {European Mathematical Society}, abstract = {We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.}, doi = {10.4171/rmi/782}, url = {http://urania.sissa.it/xmlui/handle/1963/34695}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {Boscain2013, title = {Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces}, journal = {Journal of Geometric Analysis}, volume = {23}, number = {1}, year = {2013}, month = {Jan}, pages = {438{\textendash}455}, abstract = {

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot{\textendash}Carath{\'e}odory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

}, issn = {1559-002X}, doi = {10.1007/s12220-011-9262-4}, url = {https://doi.org/10.1007/s12220-011-9262-4}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi and Mario Sigalotti} } @article {2012, title = {Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire}, volume = {29}, number = {SISSA;30/2011/M}, year = {2012}, pages = {715-735}, publisher = {Gauthier-Villars;Elsevier}, abstract = {

The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.anihpc.2012.04.001}, url = {http://hdl.handle.net/1963/4267}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2012, title = {On localization in holomorphic equivariant cohomology}, journal = {Central European Journal of Mathematics, Volume 10, Issue 4, August 2012, Pages 1442-1454}, number = {arXiv:0910.2019;}, year = {2012}, publisher = {Springer}, abstract = {We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu{\textquoteright}s localization formulas.}, keywords = {Lie algebroids}, doi = {10.2478/s11533-012-0054-2}, url = {http://hdl.handle.net/1963/6584}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {Bertola:P2poles, title = {On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev{\'e} equation}, journal = {Nonlinearity}, volume = {25}, number = {4}, year = {2012}, pages = {1179{\textendash}1185}, issn = {0951-7715}, doi = {10.1088/0951-7715/25/4/1179}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/1179}, author = {Marco Bertola} } @article {2011, title = {Large Time Existence for Thin Vibrating Plates}, journal = {Communication in Partial Differential Equations 36 (2011) 2062-2102}, number = {SISSA;59/2009/M}, year = {2011}, publisher = {Taylor \& Francis}, abstract = {We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.}, doi = {10.1080/03605302.2011.618209}, url = {http://hdl.handle.net/1963/3755}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2011, title = {Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations}, journal = {Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290}, year = {2011}, publisher = {Springer}, abstract = {We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.}, keywords = {Frobenius manifold}, doi = {10.1007/s10688-011-0030-9}, url = {http://hdl.handle.net/1963/6430}, author = {Boris Dubrovin and M.V. Pavlov and Sergei A. Zykov} } @article {2011, title = {The Liouville side of the vortex}, journal = {JHEP 09(2011)096}, number = {arXiv:1107.2787v1;}, year = {2011}, note = {25pages,11figures}, publisher = {SISSA}, abstract = {We analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.}, doi = {10.1007/JHEP09(2011)096}, url = {http://hdl.handle.net/1963/4304}, author = {Giulio Bonelli and Alessandro Tanzini and Jian Zhao} } @article {2010, title = {Lorentz Covariant k-Minkowski Spacetime}, journal = {Phys. Rev. D 81 (2010) 125024}, number = {SISSA;04/2010/FM}, year = {2010}, abstract = {In recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.}, doi = {10.1103/PhysRevD.81.125024}, url = {http://hdl.handle.net/1963/3829}, author = {Ludwik Dabrowski and Michal Godlinski and Gherardo Piacitelli} } @article {Mola2009, title = {Low-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners}, journal = {Journal of Structural Engineering}, volume = {135}, number = {7}, year = {2009}, month = {jul}, pages = {828{\textendash}835}, publisher = {American Society of Civil Engineers ({ASCE})}, doi = {10.1061/(asce)st.1943-541x.0000034}, url = {https://doi.org/10.1061/(asce)st.1943-541x.0000034}, author = {Andrea Mola and Giancarlo Bordonaro and Muhammad R. Hajj} } @article {2008, title = {Limit Time Optimal Syntheses for a control-affine system on S{\texttwosuperior}}, journal = {SIAM J. Control Optim. 47 (2008) 111-143}, number = {SISSA;48/2006/M}, year = {2008}, abstract = {For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.}, doi = {10.1137/060675988}, url = {http://hdl.handle.net/1963/1862}, author = {Paolo Mason and Rebecca Salmoni and Ugo Boscain and Yacine Chitour} } @article {2008, title = {On the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007)}, journal = {J.Phys.A: Math.Theor. 41,(2008), 205201-205247}, number = {arXiv:0801.1157;}, year = {2008}, note = {This paper appeared as a preprint in August 2007. It is published in Journal of Physics A: Mathematical and Theoretical, Volume 41, Issue 20, 6 May 2008, p. 205201-205247. It was on the archive in January 2008 (arXiv:0801.1157). This version does not differ from the published one except for two facts: 1)the addition of subsection 8.2, which proves that tr(M0Mx) = -2 for solutions y(x) \~{} a (ln x)n , n = 1, 2, x {\textrightarrow} 0. 2). The title of the journal article is : The logarithmic asymptotics of the sixth Painlev{\'e} equation}, publisher = {SISSA}, abstract = {We study the solutions of the sixth Painlev\'e equation with a logarithmic\r\nasymptotic behavior at a critical point. We compute the monodromy group\r\nassociated to the solutions by the method of monodromy preserving deformations\r\nand we characterize the asymptotic behavior in terms of the monodromy itself.}, doi = {10.1088/1751-8113/41/20/205201}, url = {http://hdl.handle.net/1963/6521}, author = {Davide Guzzetti} } @article {2007, title = {Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas}, journal = {Phys. Rev. Lett. 98 (2007) 030404}, number = {arXiv.org;cond-mat/0609346v1}, year = {2007}, abstract = {

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

}, doi = {10.1103/PhysRevLett.98.030404}, url = {http://hdl.handle.net/1963/2056}, author = {Gao Xianlong and Matteo Rizzi and Marco Polini and Rosario Fazio and Mario P. Tosi and Vivaldo L. Jr. Campo and Klaus Capelle} } @article {2006, title = {Large Parameter Behavior of Equilibrium Measures}, number = {SISSA;92/2005/FM}, year = {2006}, abstract = {We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium measure is shown to be supported on a single interval as |t| is sufficiently large. When p(x) is of an even degree, the equilibrium measure is supported on two disjoint intervals as t is negatively large; it is supported on a single interval for convex p(x) as t is positively large and is likely to be supported on multiple disjoint intervals for non-convex p(x).}, url = {http://hdl.handle.net/1963/1789}, author = {Tamara Grava and Fei-Ran Tian} } @article {2006, title = {Local Index Formula on the Equatorial Podles Sphere}, number = {SISSA;85/2005/FM}, year = {2006}, abstract = {We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the {\textquoteleft}degenerate\\\' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one....}, doi = {10.1007/s11005-005-0047-1}, url = {http://hdl.handle.net/1963/1782}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski} } @article {2005, title = {The local index formula for SUq(2)}, journal = {K-Theory 35 (2005) 375-394}, number = {SISSA;01/2005/FM}, year = {2005}, abstract = {We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.}, doi = {10.1007/s10977-005-3116-4}, url = {http://hdl.handle.net/1963/1713}, author = {Walter van Suijlekom and Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Joseph C. Varilly} } @article {2003, title = {A lemma and a conjecture on the cost of rearrangements}, journal = {Rend. Sem. Mat. Univ. Padova 110 (2003) 97-102}, number = {SISSA;13/2003/M}, year = {2003}, publisher = {Universit{\`a} di Padova}, abstract = {Consider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement.}, url = {http://hdl.handle.net/1963/2914}, author = {Alberto Bressan} } @article {2003, title = {On the local structure of optimal trajectories in R3}, journal = {SIAM J. Control Optim. 42 (2003) 513-531}, number = {SISSA;41/2002/M}, year = {2003}, publisher = {SISSA Library}, abstract = {We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.}, doi = {10.1137/S0363012902409246}, url = {http://hdl.handle.net/1963/1612}, author = {Andrei A. Agrachev and Mario Sigalotti} } @article {2002, title = {Linearized elasticity as gamma-limit of finite elasticity}, journal = {Set-Valued Anal. 10 (2002), p.165-183}, number = {SISSA;69/2001/M}, year = {2002}, publisher = {Springer}, doi = {10.1023/A:1016577431636}, url = {http://hdl.handle.net/1963/3052}, author = {Gianni Dal Maso and Matteo Negri and Danilo Percivale} } @article {2002, title = {Local calibrations for minimizers of the Mumford-Shah functional with a triple junction}, journal = {Commun. Contemp. Math. 4 (2002) 297-326}, number = {SISSA;39/2001/M}, year = {2002}, publisher = {World Scientific}, abstract = {We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method.}, doi = {10.1142/S0219199702000646}, url = {http://hdl.handle.net/1963/3050}, author = {Maria Giovanna Mora} } @article {2002, title = {On a Lyapunov functional relating shortening curves and viscous conservation laws}, journal = {Nonlinear Anal. 51 (2002) 649-662}, number = {SISSA;123/99/M}, year = {2002}, publisher = {Elsevier}, abstract = {We study a nonlinear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the \\\"change of shape\\\" of a BV solution to a scalar conservation law.}, doi = {10.1016/S0362-546X(01)00848-3}, url = {http://hdl.handle.net/1963/1337}, author = {Stefano Bianchini and Alberto Bressan} } @article {2001, title = {Lax representation and Poisson geometry of the Kowalevski top}, journal = {J. Phys. A 34 (2001) 2077-2085}, number = {SISSA;70/2000/FM}, year = {2001}, publisher = {IOP Publishing}, abstract = {We discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel\\\'fand-Zakharevich bi-Hamiltonian setting for integrable systems.}, doi = {10.1088/0305-4470/34/11/301}, url = {http://hdl.handle.net/1963/3244}, author = {Gregorio Falqui} } @article {Bertola:LietripleRMA, title = {Lie triple systems and warped products}, journal = {Rend. Mat. Appl. (7)}, volume = {21}, number = {1-4}, year = {2001}, pages = {275{\textendash}293}, issn = {1120-7183}, author = {Marco Bertola and Gouthier, D.} } @article {2001, title = {Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set}, journal = {Ann. I. H. Poincare - An., 2001, 18, 403}, number = {SISSA;21/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1016/S0294-1449(01)00075-0}, url = {http://hdl.handle.net/1963/1479}, author = {Maria Giovanna Mora and Massimiliano Morini} } @article {2000, title = {Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets}, journal = {J. Math. Pures Appl. 79, 2 (2000) 141-162}, number = {SISSA;47/99/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0021-7824(99)00140-3}, url = {http://hdl.handle.net/1963/1261}, author = {Gianni Dal Maso and Maria Giovanna Mora and Massimiliano Morini} } @article {1999, title = {L-1 stability estimates for n x n conservation laws}, journal = {Arch. Ration. Mech. Anal. 149 (1999), no. 1, 1--22}, number = {SISSA;80/98/M}, year = {1999}, publisher = {Springer}, abstract = {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 {\textquoteleft}almost decreasing\\\', i.e., $\\\\Phi(u(t),v(t))-\\\\Phi(u(s),v(s))\\\\leq\\\\break O (\\\\epsilon){\textperiodcentered}(t-s)$ 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.\\\'\\\'}, doi = {10.1007/s002050050165}, url = {http://hdl.handle.net/1963/3373}, author = {Alberto Bressan and Tai-Ping Liu and Tong Yang} } @article {1999, title = {A Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient}, journal = {Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717}, year = {1999}, publisher = {SISSA}, abstract = {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.}, doi = {10.1016/S0362-546X(98)00067-4}, url = {http://hdl.handle.net/1963/6439}, author = {Gianni Dal Maso and Vladimir V. Goncharov and Antonio Ornelas} } @article {1998, title = {Limits of variational problems for Dirichlet forms in varying domains}, journal = {Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116}, year = {1998}, publisher = {SISSA}, doi = {10.1016/S0362-546X(98)00067-4}, url = {http://hdl.handle.net/1963/6440}, author = {Gianni Dal Maso and Virginia De Cicco and Lino Notarantonio and Nicoletta A. Tchou} } @article {1994, title = {Limits of Dirichlet problems in perforated domains: a new formulation}, journal = {Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360}, number = {SISSA;167/1994/M}, year = {1994}, publisher = {Universit{\`a} degli Studi di Trieste, Dipartimento di Scienze Matematiche}, url = {http://hdl.handle.net/1963/3649}, author = {Gianni Dal Maso and Rodica Toader} } @article {1989, title = {Limits of obstacle problems for the area functional.}, journal = {Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309}, number = {SISSA;96/87/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/577}, author = {Gianni Dal Maso and G. Carere and Antonio Leaci and Eduardo Pascali} } @article {1988, title = {Limits of nonlinear Dirichlet problems in varying domains.}, journal = {Manuscripta Math. 61 (1988), no. 3, 251-278.}, number = {SISSA;54/87/A}, year = {1988}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/536}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1987, title = {Lie algebra extensions and abelian monopoles.}, journal = {Phys. Lett. B 195 (1987), no. 3, 429-434}, number = {SISSA;25/87/FM}, year = {1987}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(87)90043-8}, url = {http://hdl.handle.net/1963/506}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1987, title = {Limits of nonlinear Dirichlet problems in varying domains. (Italian)}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118}, number = {SISSA;4/87/M}, year = {1987}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/486}, author = {Gianni Dal Maso and Anneliese Defranceschi} }