American Institute of Mathematical Sciences

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