Periodic Homogenization of Green and Neumann Functions

Carlos Kenig; Fanghua Lin; Zhongwei Shen

doi:10.1002/cpa.21482

Periodic Homogenization of Green and Neumann Functions

Carlos Kenig, Fanghua Lin, Zhongwei Shen

Mathematics

Research output: Contribution to journal › Article › peer-review

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 L^p and W^1,p for solutions with Dirichlet or Neumann boundary conditions.

Original language	English (US)
Pages (from-to)	1219-1262
Number of pages	44
Journal	Communications on Pure and Applied Mathematics
Volume	67
Issue number	8
DOIs	https://doi.org/10.1002/cpa.21482
State	Published - Aug 2014

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Mathematics(all)
Applied Mathematics

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10.1002/cpa.21482

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title = "Periodic Homogenization of Green and Neumann Functions",

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.",

author = "Carlos Kenig and Fanghua Lin and Zhongwei Shen",

year = "2014",

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AB - 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.

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Periodic Homogenization of Green and Neumann Functions

Abstract

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