Homogenization of obstacle problems in Orlicz-Sobolev spaces

TL;DR

This paper investigates the homogenization process for obstacle problems within Orlicz-Sobolev spaces, focusing on a broad class of monotone operators, and establishes convergence of solutions and coincidence sets using Lewy-Stampacchia inequalities.

Contribution

It introduces a new homogenization framework for obstacle problems in Orlicz-Sobolev spaces with general monotone operators, extending previous results to degenerate and singular cases.

Findings

Established homogenization results for obstacle problems in Orlicz-Sobolev spaces.

Proved convergence of solutions and coincidence sets under non-degeneracy.

Applied Lewy-Stampacchia inequalities to facilitate compactness arguments.

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.