Periodic Homogenization of Green and Neumann Functions | Zendy

Kenig Carlos | Zendy; Lin Fanghua | Zendy; Shen Zhongwei | Zendy

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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.

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