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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.

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
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