Periodic Homogenization of Green and Neumann Functions |
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| Authors: | Carlos Kenig Fanghua Lin Zhongwei Shen |
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| Institution: | 1. Department of Mathematics, University of Chicago, Chicago, IL, USA;2. Courant Institute, New York, NY, USA;3. Department of Mathematics, University of Kentucky, Lexington, KY, USA |
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| 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. © 2014 Wiley Periodicals, Inc. |
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