Boundary Korn Inequality and Neumann Problems in Homogenization of   Systems of Elasticity
  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}. 
Jun Geng, Zhongwei Shen, and Liang Song
math.AP