Homogenization of Elliptic Systems with Neumann Boundary Conditions

Abstract

The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators $\{{\mathcal{L}}_{\epsilon },\epsilon >0\}$, arising in the theory of homogenization, with rapidly oscillating periodic coefficients. We establish sharp $W^{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates, which are uniform in the parameter $\epsilon$, on solutions with Neumann boundary conditions in $C^{1,\hat{I}\pm }$ domains.

39 pages