Periodic Homogenization of Green and Neumann Functions

Carlos Kenig, Fang-Hua 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 - 2014

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Periodic Homogenization
Neumann function
Poisson Kernel
Oscillating Coefficients
Dirichlet-to-Neumann Map
Optimal Convergence Rate
Periodic Coefficients
Corrector
Neumann Boundary Conditions
Elliptic Operator
Dirichlet Boundary Conditions
Dirichlet
Asymptotic Expansion
Mathematical operators
Green's function
Asymptotic Behavior
Boundary conditions
Family

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Periodic Homogenization of Green and Neumann Functions. / Kenig, Carlos; Lin, Fang-Hua; Shen, Zhongwei.

In: Communications on Pure and Applied Mathematics, Vol. 67, No. 8, 2014, p. 1219-1262.

Research output: Contribution to journalArticle

Kenig, Carlos ; Lin, Fang-Hua ; Shen, Zhongwei. / Periodic Homogenization of Green and Neumann Functions. In: Communications on Pure and Applied Mathematics. 2014 ; Vol. 67, No. 8. pp. 1219-1262.
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