Abstract: This talk 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, a large-scale Rellich estimate obtained by Shen and some techniques of harmonic analysis. This is a joint work with Jun Geng and Zhongwei Shen.
