Periodic Homogenization of Green and Neumann Functions

Carlos Kenig, Fanghua Lin, Zhongwei Shen

Research output: Contribution to journalArticlepeer-review

75 Scopus citations

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

Funding

FundersFunder number
National Science Foundation Arctic Social Science ProgramDMS-0855294., DMS-0968472, DMS-0700517
Directorate for Mathematical and Physical Sciences0700517, 0968472, 0855294

    ASJC Scopus subject areas

    • General Mathematics
    • Applied Mathematics

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