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Archive for Rational Mechanics and Analysis

, Volume 203, Issue 3, pp 1009–1036 | Cite as

Convergence Rates in L 2 for Elliptic Homogenization Problems

  • Carlos E. Kenig
  • Fanghua LinEmail author
  • Zhongwei Shen
Article

Abstract

We study rates of convergence of solutions in L 2 and H 1/2 for a family of elliptic systems \({\{\mathcal{L}_\varepsilon\}}\) 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 \({\{\mathcal{L}_\varepsilon\}}\) . 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.

Keywords

Weak Solution Convergence Rate Dirichlet Problem Neumann Boundary Condition Neumann Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.Department of MathematicsUniversity of KentuckyLexingtonUSA

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