Asymptotic behavior of elliptic problems in perforated domains with nonlinear boundary conditions

Article type: Research Article

Authors: Cioranescu, Doina | Donato, Patrizia^; | Zaki, Rachad

Affiliations: Laboratoire Jacques-Louis Lions, UMR CNRS 7598, BP 187, 4 Place Jussieu, 75252 Paris Cedex 05, France E-mails: {cioran, zaki}@ann.jussieu.fr | Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Avenue de l'Université, BP 12, 76801 Saint Etienne de Rouvray, France E-mail: [email protected]

Abstract: In this paper, we apply the periodic unfolding method in perforated domains introduced by Cioranescu et al. (Portugal. Math. 63(4) (2006), 467–496) to a class of elliptic problems with nonlinear conditions on the boundary of the holes. A new compactness result will play a major role in the homogenization process and provides correctors without using any extension operator.

Journal: Asymptotic Analysis, vol. 53, no. 4, pp. 209-235, 2007