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Periodic Homogenization of Green and Neumann Functions
Author(s) -
Kenig Carlos,
Lin Fanghua,
Shen Zhongwei
Publication year - 2014
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21482
Subject(s) - homogenization (climate) , mathematics , von neumann architecture , mathematical analysis , pure mathematics , biodiversity , ecology , biology
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. © 2014 Wiley Periodicals, Inc.