Affiliations: Normandie Université, Université de Rouen, Laboratoire de Mathématiques Raphaël Salem, CNRS, UMR 6085, Avenue de l'Université, BP 12, 76801 Saint-Étienne du Rouvray cedex, France. E-mails: ichourabi@yahoo.fr, Patrizia.Donato@univ-rouen.fr
Abstract: In this paper, we study the homogenization and the correctors for a class of linear elliptic problems in a periodically perforated domain when the oscillating matrix field also depend on a weakly converging sequence. We prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. Using the periodic unfolding method, we first derive the homogenized problem, then we study the convergence of the energy of the solution and the related corrector, which are the main results of this paper. As a particular case, we obtain a corrector result for the Laplacian with a linear nonhomogeneous Neumann condition on the hole, in the case of a nonzero Neumann data with a zero average. This remained an open problem since the corresponding homogenized results given in [Asymptotic Anal. 1 (1988), 115–138].
