Uniform W1,P estimates and large-scale regularity for Dirichlet problems in perforated domains

被引：3

作者：

Shen, Zhongwei ^{[1
]}

Wallace, Jamison ^{[1
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2023年 / 285卷 / 10期

关键词：

Uniform estimates; Large-scale regularity; Perforated domain; Homogenization; HOMOGENIZATION;

D O I：

10.1016/j.jfa.2023.110118

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the Dirichlet problem for Laplace's equation in a domain w & epsilon;,& eta; perforated periodically with small holes in Rd, where E represents the scale of the minimal distances between holes and n the ratio between the scale of sizes of holes and E. We establish W1,p estimates for solutions with bounding constants depending explicitly on E and n. The proof relies on a large-scale Lipschitz estimate for harmonic functions in perforated domains. The results are optimal for d & GE; 2.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：33

共 11 条

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