Boundary estimates in homogenization of systems of elasticity on Lipschitz domains: Lp theory

Abstract

The primary purpose of this paper is to investigate a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization in Lipschitz domains. As a consequence, for d≥4, we prove that the Lp Neumann and Lp Dirichlet boundary value problems for systems of second order linear elasticity are uniquely solvable for 2(d−1)d+1−δ<p<2+δ and 2−δ<p<2(d−1)d−3+δ respectively.