Two-Scale Regularity for Homogenization Problems with Non-Smooth Fine Scale Geometry

Abstract

Elliptic problems on unbounded domains with periodic coefficients and geometries are analyzed and two-scale regularity results for the solution are given. These are based on a detailed analysis in weighted Sobolev spaces of the so-called unit-cell problem, in which the critical parameters (the period $\epsilon$, the wavenumber t, and the differentiation order) enter explicitly.