Homogenization of Boundary Value Problems in Perforated Lipschitz Domains

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.

44 pages

References in corpus (2)

• Elliptic regularity and quantitative homogenization on percolation clusters
• Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity