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 optimal convergence rates in Lp and W1,p for solutions with Dirichlet or Neumann boundary conditions.
Original language | English (US) |
---|---|
Pages (from-to) | 1219-1262 |
Number of pages | 44 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 67 |
Issue number | 8 |
DOIs | |
State | Published - Aug 2014 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics