Uniform regularity for degenerate elliptic equations in perforated domains

Zhongwei Shen; Jinping Zhuge

Uniform regularity for degenerate elliptic equations in perforated domains

Analysis of PDEs 2023-11-20 v1

Authors: Zhongwei Shen , Jinping Zhuge

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.

Keywords

degenerate elliptic equations perforated domains oscillating coefficients quantitative convergence rate weighted lipschitz estimates w^{1,p} estimates

Cite

@article{arxiv.2311.10258,
  title  = {Uniform regularity for degenerate elliptic equations in perforated domains},
  author = {Zhongwei Shen and Jinping Zhuge},
  journal= {arXiv preprint arXiv:2311.10258},
  year   = {2023}
}

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39 pages

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