| Affiliation: | 1.Department of Mathematics,University of Chicago,Chicago,USA;2.Courant Institute of Mathematical Sciences,New York University,New York,USA;3.Department of Mathematics,University of Kentucky,Lexington,USA |
| Abstract: | We study rates of convergence of solutions in L 2 and H 1/2 for a family of elliptic systems {Le}{{mathcal{L}_varepsilon}} with rapidly 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 {Le}{{mathcal{L}_varepsilon}} . Most of our results, which rely on the recently established uniform estimates for the L 2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. |
