Uniform Estimates for Dirichlet Problems in Perforated Domains

2022/08/25 by Shen, Zhongwei
#35B27 #35J05 #35J25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.12198

Abstract

This paper studies the Dirichlet problem for Laplace's equation in a domain Ω_{ε, η} perforated with small holes, where ε represents the scale of the minimal distances between holes and η the ratio between the scale of sizes of holes and ε. We establish W^{1, p} estimates for solutions with bounding constants depending explicitly on the small parameters ε and η. We also show that these estimates are either optimal or near optimal.

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