Homogenization of Green and Neumann Functions

Details Homogenization of Green and Neumann Functions Homogenization of Green and Neumann Functions

2012-01-06

arxiv.org/abs/1201.1440v1

Mathematics

Analysis of PDEs

35 pages

Scientific paper

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.

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