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Portugaliae Mathematica

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Volume 75, Issue 3/4, 2018, pp. 267–283
DOI: 10.4171/PM/2019

Published online: 2019-06-06

Homogenization of obstacle problems in Orlicz–Sobolev spaces

Diego Marcon[1], José Francisco Rodrigues[2] and Rafayel Teymurazyan[3]

(1) Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
(2) Universidade de Lisboa, Portugal
(3) Universidade de Coimbra, Portugal

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.

Keywords: Homogenization, obstacle problem, Orlicz–Sobolev spaces, convergence of coincidence sets

Marcon Diego, Rodrigues José Francisco, Teymurazyan Rafayel: Homogenization of obstacle problems in Orlicz–Sobolev spaces. Port. Math. 75 (2018), 267-283. doi: 10.4171/PM/2019