Uniform regularity for degenerate elliptic equations in perforated domains

Zhongwei Shen; Jinping Zhuge

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arXiv · 2311.10258

Uniform regularity for degenerate elliptic equations in perforated domains

Zhongwei Shen·Jinping Zhuge

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Abstract

This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectrum problems for uniformly elliptic equations in perforated domains. We establish a quantitative convergence rate and obtain the uniform weighted Lipschitz and $W^{1,p}$ estimates.

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Zhongwei Shen, Jinping Zhuge. 2023-11-17. Uniform regularity for degenerate elliptic equations in perforated domains. https://arxiv.org/abs/2311.10258

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