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

Producción científica: Article › revisión exhaustiva

80 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	1219-1262
Número de páginas	44
Publicación	Communications on Pure and Applied Mathematics
Volumen	67
N.º	8
DOI	https://doi.org/10.1002/cpa.21482
Estado	Published - ago 2014

Financiación

Financiadores	Número del financiador
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	0700517
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-0855294., DMS-0968472, DMS-0700517
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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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.",

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Periodic Homogenization of Green and Neumann Functions

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