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 Lp and W1,p for solutions with Dirichlet or Neumann boundary conditions.
|Original language||English (US)|
|Number of pages||44|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Aug 2014|
ASJC Scopus subject areas
- Applied Mathematics