Homogenization of Green and Neumann Functions

Carlos E. Kenig; Fanghua Lin; Zhongwei Shen

Homogenization of Green and Neumann Functions

Analysis of PDEs 2012-01-09 v1

Authors: Carlos E. Kenig , Fanghua Lin , Zhongwei Shen

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 near optimal convergence rates in $W^{1,p}$ for solutions with Dirichlet or Neumann boundary conditions.

Keywords

homogenization Green function Neumann function periodic coefficients Dirichlet corrector Neumann corrector Poisson kernel convergence rates

Cite

@article{arxiv.1201.1440,
  title  = {Homogenization of Green and Neumann Functions},
  author = {Carlos E. Kenig and Fanghua Lin and Zhongwei Shen},
  journal= {arXiv preprint arXiv:1201.1440},
  year   = {2012}
}

Comments

35 pages

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