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On etudie l'homogeneisation stochastique non lineaire d'une classe de fonctionnelles integrales. On relie le probleme a la theorie ergodique
Abstract. 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… (More)
Abstract. The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of $\Gamma$-convergence by a sequence of non-local integral functionals.
Abstract. We show that discrete models of atoms subject to nearest‐neighbour non‐linear interactions approximate continua allowing for softening and fracture. A detailed study of local minima and… (More)
Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has… (More)
Within the context of heteroepitaxial growth of a film onto a substrate, terraces and steps self-organize according to misfit elasticity forces. Discrete models of this behavior were developed by… (More)
We study the general form of the limit, in the sense of Γ-convergence, of a sequence of nonlinear variational problems in varying domains with Dirichlet boundary conditions. The asymptotic problem is… (More)
The asymptotic behavior of an anisotropic Cahn–Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $$\varepsilon $$ε that determines the width of… (More)
Abstract We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G. A. Francfort and J.-J. Marigo, and based on… (More)