Homogenization of Boundary Value Problems in Perforated Lipschitz Domains

TL;DR

This paper develops uniform boundary regularity estimates for elliptic equations with oscillating, high-contrast coefficients in perforated Lipschitz domains, advancing homogenization theory.

Contribution

It establishes uniform nontangential-maximal-function estimates for boundary value problems in perforated Lipschitz domains with oscillating coefficients.

Findings

Proved uniform estimates for Dirichlet, regularity, and Neumann problems

Extended boundary regularity results to perforated Lipschitz domains

Enhanced understanding of homogenization in complex geometries

Abstract

This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet, regularity, and Neumann problems with $L^2$ boundary data in a periodically perforated Lipschitz domain.