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<p>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 <i>W</i><sup>1,<i>p</i></sup> estimates.</p>

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Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains

  • 期刊论文

  • 发表日期：

    2025年1月15日

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  • Zhongwei Shen,
  • Jinping Zhuge

摘要

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 W1,p estimates.