Periodic Homogenization of Green and Neumann Functions

被引：90

作者：

Kenig, Carlos E. ^{[1
]}

Lin, Fanghua ^{[2
]}

Shen, Zhongwei ^{[3
]}

机构：

[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[2] NYU, Courant Inst, New York, NY 10012 USA

[3] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2014年 / 67卷 / 08期

基金：

美国国家科学基金会;

关键词：

BOUNDARY-VALUE-PROBLEMS; DIRICHLET PROBLEM; COMPACTNESS METHODS; LIPSCHITZ; EQUATION;

D O I：

10.1002/cpa.21482

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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,W-p for solutions with Dirichlet or Neumann boundary conditions. (C) 2014 Wiley Periodicals, Inc.

引用

页码：1219 / 1262

页数：44

共 27 条

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