Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem
Antonin Chambolle, ,CMAP, Ecole Polytechnique, CNRS, 91128 Palaiseau, Gilles Thouroude, ,Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05 · Networks and Heterogeneous Media · 2009
We consider the homogenization of a periodic interfacialenergy, such as considered in recents papers byCaffarelli and De La Llave [14],or Dirr, Lucia and Novaga [16].In particular, we include the case where an external forcingfield (which is unbounded in the limit) is present, and suggest two differentways to take care of this additional perturbation.We provide a proof of a $\Gamma$-limit,however, we also observe that thanks to the coarea formula, in manycases such a result is already known in the framework of $BV$ homogenization.This leads to an interesting new construction for the plane-likeminimizers in periodic media of Caffarelli and De La Llave, througha cell problem.