"Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem" - Archive ouverte HAL Access content directly
Journal Articles Networks and Heterogeneous Media Year : 2009

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

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Abstract

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.

Dates and versions

hal-00381326 , version 1 (05-05-2009)

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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), pp.127-152. ⟨10.3934/nhm.2009.4.127⟩. ⟨hal-00381326⟩
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