Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

Abstract

This paper concerns with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with $L^2$ boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in \cite{Shen-2016}.

32 pages

References in corpus (1)

• The L^p Boundary Value Problems on Lipschitz Domains

Cited by in corpus (4)

• The Methods of Layer Potentials for General Elliptic Homogenization Problems in Lipschitz Domains
• Quantitative Estimates in Homogenization of Parabolic Systems of Elasticity in Lipschitz Cylinders
• Optimal Boundary Estimates for Stokes Systems in Homogenization Theory
• Homogenization of Boundary Value Problems in Perforated Lipschitz Domains