%0 Journal Article
%T Homogenization of Elliptic Systems with Neumann Boundary Conditions
%A Carlos E. Kenig
%A Fanghua Lin
%A Zhongwei Shen
%J Mathematics
%D 2010
%I arXiv
%X The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators $\{\mathcal{L}_\varepsilon, \varepsilon>0\}$, 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 $\varepsilon$, on solutions with Neumann boundary conditions in $C^{1,\alpha}$ domains.
%U http://arxiv.org/abs/1010.6114v1