VARIATIONAL APPROXIMATION OF INTERFACE ENERGIES AND APPLICATIONS

Samuel Amstutz (1, 2) , Daniel Gourion (1) , Mohammed Zabiba (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Minimal partition problems consist in finding a partition of a domain into a given number of components in order to minimize a geometric criterion. In applicative fields such as image processing or continuum mechanics, it is standard to incorporate in this objective an interface energy that accounts for the lengths of the interfaces between components. The present work is focused on the theoretical and numerical treatment of minimal partition problems with such interface energies. The considered approach is based on a Γ-convergence approximation combined with convex analysis techniques.

Domaines: Optimisation et contrôle [math.OC]

Samuel Amstutz, Daniel Gourion, Mohammed Zabiba. VARIATIONAL APPROXIMATION OF INTERFACE ENERGIES AND APPLICATIONS. Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, 2021, Interfaces and Free Boundaries, 23, pp.59-102. ⟨hal-02390079v2⟩