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.

中文翻译：

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Orlicz-Sobolev 空间中障碍问题的同质化

我们研究了 Orlicz-Sobolev 空间中各种 $p(\cdot)$-Laplacian 类型的单调算子（可能是退化的或奇异的）的障碍问题的同质化。我们的方法基于 Lewy-Stampacchia 不等式，然后可以使用紧凑性论证。我们还证明了非简并条件下重合集的收敛性。