Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 63, No. 4, pp. 467-496 (2006)

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The periodic unfolding method in perforated domains

Doina Cioranescu, Patrizia Donato and Rachad Zaki

Laboratoire Jacques-Louis Lions, UMR CNRS 7598, BP 187,
4 Place Jussieu, 75252 Paris Cedex 05 -- FRANCE
E-mail: cioran@ann.jussieu.fr
Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085,
Avenue de l'Université, BP 12, 76801 Saint Etienne de Rouvray -- FRANCE
and Laboratoire Jacques-Louis Lions, UMR CNRS 7598, BP 187,
4 Place Jussieu, 75252 Paris Cedex 05 -- FRANCE
E-mail: patrizia.donato@univ-rouen.fr
Laboratoire Jacques-Louis Lions, UMR CNRS 7598, BP 187,
4 Place Jussieu, 75252 Paris Cedex 05 -- FRANCE
E-mail: zaki@ann.jussieu.fr

Abstract: The periodic unfolding method was introduced in [4] by D. Cioranescu, A. Damlamian and G. Griso for the study of classical periodic homogenization. The main tools are the unfolding operator and a macro-micro decomposition of functions which allows to separate the macroscopic and microscopic scales.
In this paper, we extend this method to the homogenization in domains with holes, introducing the unfolding operator for functions defined on periodically perforated domains as well as a boundary unfolding operator.
As an application, we study the homogenization of some elliptic problems with a Robin condition on the boundary of the holes, proving convergence and corrector results.

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Electronic version published on: 7 Mar 2008.

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