Uniform $W^{1,p}$ Estimates and Large-Scale Regularity for Dirichlet Problems in Perforated Domains

Zhongwei Shen, Jamison Wallace

In this paper we study the Dirichlet problem for Laplace's equation in a domain ${\omega }_{\epsilon ,\eta }$ perforated periodically with small holes in ${\mathbb{R}}^d$, where $\epsilon$ represents the scal…