Layer potential methods for elliptic homogenization problems

Carlos E. Kenig, Zhongwei Shen

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

In this paper we use the method of layer potentials to study L2 boundary value problems in a bounded Lipschitz domain Ω for a family of second-order elliptic systems with rapidly oscillating periodic coefficients. Defining, under the assumption that A(X) is elliptic, symmetric, periodic, and Hölder-continuous, we establish the solvability of the L2 Dirichlet, regularity, and Neumann problems for in Ω with optimal estimates uniform in ε>0.

Original languageEnglish
Pages (from-to)1-44
Number of pages44
JournalCommunications on Pure and Applied Mathematics
Volume64
Issue number1
DOIs
StatePublished - Jan 2011

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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