Convergence Rates in L^2 for Elliptic Homogenization Problems

Details Convergence Rates in L^2 for Elliptic Homogenization Problems Convergence Rates in L^2 for Elliptic Homogenization Problems

2011-02-28

arxiv.org/abs/1103.0023v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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.

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