## Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem.(English)Zbl 1186.35013

The authors consider the homogenization of a periodic surface energy combined with (exploding in the limit $$\epsilon\to 0$$) bulk forcing term. After appropriate rescaling of the total energy, they show convergence (in the homogenization limit) to an anisotropic perimeter with interfacial energy characterized by the energies of plane-like minimizers in balls of large volume. The proof is based on $$\Gamma$$-convergence type arguments.

### MSC:

 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 74Q05 Homogenization in equilibrium problems of solid mechanics 49Q20 Variational problems in a geometric measure-theoretic setting 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

### Keywords:

$$\Gamma$$-convergence; minimal surfaces; BV functions
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