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 |
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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 |
Funding
Funders | Funder number |
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National Science Foundation Arctic Social Science Program | DMS-0855294., DMS-0968472, DMS-0700517 |
Directorate for Mathematical and Physical Sciences | 0700517, 0968472, 0855294 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics