Homogenization of obstacle problems in Orlicz–Sobolev spaces

Abstract

We study the homogenization of obstacle problems in Orlicz–Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the $p(\cdot )$-Laplacian type. Our approach is based on the Lewy–Stampacchia inequalities, which then give access to a compactness argument. We also prove the convergence of the coincidence sets under non-degeneracy conditions.