Periodic Homogenization of Green and Neumann Functions

Carlos Kenig, Fanghua Lin, Zhongwei Shen

Research output: Contribution to journalArticle

Abstract

For a family of second-order elliptic operators with rapidly oscillating periodic coefficients, we study the asymptotic behavior of the Green and Neumann functions, using Dirichlet and Neumann correctors. As a result we obtain asymptotic expansions of Poisson kernels and the Dirichlet-to-Neumann maps as well as optimal convergence rates in Lp and W1,p for solutions with Dirichlet or Neumann boundary conditions.

Original languageEnglish (US)
Pages (from-to)1219-1262
Number of pages44
JournalCommunications on Pure and Applied Mathematics
Volume67
Issue number8
DOIs
StatePublished - Aug 2014

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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