TITLE:  Boundary Korn Inequality and Neumann Problems in Homogenization of Elliptic Systems of Elasticity

 

ABSTRACT:  This talk concerns with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coecients, arising in the theory of homogenization.  We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity

and uses a large-scale Rellich estimate. This is a joint work with Jun Geng and Liang Song.