Convergence Rates in Periodic Homogenization of Systems of Elasticity

TL;DR

This paper investigates the rate at which solutions to systems of linear elasticity with periodic coefficients converge to their homogenized limits, providing precise convergence estimates in the $L^2$ norm for boundary value problems.

Contribution

It establishes sharp $L^2$ convergence rates for periodic homogenization of elasticity systems with measurable coefficients, advancing theoretical understanding of convergence behavior.

Findings

Sharp $L^2$ convergence rates proved

Applicable to systems with bounded measurable coefficients

Enhances theoretical framework for elasticity homogenization

Abstract

This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable coefficients.