March  2009, 4(1): 127-152. doi: 10.3934/nhm.2009.4.127

Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem

1. 

CMAP, Ecole Polytechnique, CNRS, 91128 Palaiseau, France

2. 

Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France

Received  July 2008 Revised  January 2009 Published  February 2009

We consider the homogenization of a periodic interfacial energy, such as considered in recents papers by Caffarelli and De La Llave [14], or Dirr, Lucia and Novaga [16]. In particular, we include the case where an external forcing field (which is unbounded in the limit) is present, and suggest two different ways 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 many cases such a result is already known in the framework of $BV$ homogenization. This leads to an interesting new construction for the plane-like minimizers in periodic media of Caffarelli and De La Llave, through a cell problem.
Citation: Antonin Chambolle, Gilles Thouroude. Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem. Networks and Heterogeneous Media, 2009, 4 (1) : 127-152. doi: 10.3934/nhm.2009.4.127
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