Convergence Rates in L 2 for Elliptic Homogenization Problems

Carlos E. Kenig, Fang-Hua Lin, Zhongwei Shen

Research output: Contribution to journalArticle

Abstract

We study rates of convergence of solutions in L 2 and H 1/2 for a family of elliptic systems {L e{open}} 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 {L e{open}}. 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.

Original languageEnglish (US)
Pages (from-to)1009-1036
Number of pages28
JournalArchive for Rational Mechanics and Analysis
Volume203
Issue number3
DOIs
Publication statusPublished - Mar 2012

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ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

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