%0 Journal Article
%T Convergence Rates in L^2 for Elliptic Homogenization Problems
%A Carlos E. Kenig
%A Fanghua Lin
%A Zhongwei Shen
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s00205-011-0469-0
%X We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {L_\epsilon}. Most of our results, which rely on the recently established uniform estimates for the L^2 Dirichlet and Neumann problems in \cite{12,13}, are new even for smooth domains.
%U http://arxiv.org/abs/1103.0023v1