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


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.


Weak Solution Convergence Rate Dirichlet Problem Neumann Boundary Condition Neumann Problem 
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© 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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