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

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.