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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.
Kenig et al. (Thu,) studied this question.
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