TY - JOUR
T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I
JF - Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337
Y1 - 2016
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Laura Caravenna
PB - Elsevier
UR - http://urania.sissa.it/xmlui/handle/1963/35207
U1 - 35507
U2 - Mathematics
ER -
TY - RPRT
T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II
Y1 - 2016
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Laura Caravenna
UR - http://urania.sissa.it/xmlui/handle/1963/35197
U1 - 35494
U2 - Mathematics
ER -
TY - JOUR
T1 - On the Lp-differentiability of certain classes of functions
Y1 - 2014
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Gianluca Crippa
AB - 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.
PB - European Mathematical Society
UR - http://urania.sissa.it/xmlui/handle/1963/34695
U1 - 34909
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -
TY - CHAP
T1 - Reduction on characteristics for continuous of a scalar balance law
T2 - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406
Y1 - 2014
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Laura Caravenna
KW - Method of characteristics
JF - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406
PB - SISSA
UR - http://hdl.handle.net/1963/6562
U1 - 6516
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday
Y1 - 2014
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Gianluca Crippa
AB - We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.
PB - European Mathematical Society; Springer Verlag
UR - http://urania.sissa.it/xmlui/handle/1963/34692
U1 - 34906
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Quasistatic evolution of sessile drops and contact angle hysteresis
JF - Arch. Rational Mech. Anal. 202 (2011) 295-348
Y1 - 2011
A1 - Giovanni Alberti
A1 - Antonio DeSimone
AB - We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.
PB - Springer
UR - http://hdl.handle.net/1963/4912
U1 - 4693
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -
TY - RPRT
T1 - Structure of level sets and Sard-type properties of Lipschitz maps
Y1 - 2011
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Gianluca Crippa
PB - SISSA
UR - http://hdl.handle.net/1963/4657
U1 - 4424
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -
TY - RPRT
T1 - A uniqueness result for the continuity equation in two dimensions
Y1 - 2011
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Gianluca Crippa
PB - SISSA
UR - http://hdl.handle.net/1963/4663
U1 - 4425
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -
TY - JOUR
T1 - Wetting of rough surfaces: a homogenization approach
JF - Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97
Y1 - 2005
A1 - Antonio DeSimone
A1 - Giovanni Alberti
AB - The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.
UR - http://hdl.handle.net/1963/2253
U1 - 1994
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - The calibration method for the Mumford-Shah functional and free-discontinuity problems
JF - Calc. Var. Partial Differential Equations 16 (2003) 299-333
Y1 - 2003
A1 - Giovanni Alberti
A1 - Guy Bouchitte
A1 - Gianni Dal Maso
AB - We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.
PB - Springer
UR - http://hdl.handle.net/1963/3051
U1 - 1282
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - The calibration method for the Mumford-Shah functional
JF - C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254
Y1 - 1999
A1 - Giovanni Alberti
A1 - Guy Bouchitte
A1 - Gianni Dal Maso
AB - 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).
PB - Elsevier
UR - http://hdl.handle.net/1963/1235
U1 - 2708
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -