Convergence Rates in L 2 for Elliptic Homogenization Problems

Carlos E. Kenig, Fanghua Lin, Zhongwei Shen

Research output: Contribution to journalArticlepeer-review

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
StatePublished - Mar 2012

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Convergence Rates in L <sup>2</sup> for Elliptic Homogenization Problems'. Together they form a unique fingerprint.

Cite this