Homogenization of Green and Neumann Functions

2012/01/06 by Carlos E. Kenig, Fanghua Lin, Kenig, Carlos E. +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1201.1440

35 pages

arxiv created 2012/01/06 · openalex publication_date 2012/01/06 · arxiv updated 2012/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 near optimal convergence rates in W^1,p for solutions with Dirichlet or Neumann boundary conditions.

Cited by

• Recent progress in the theory of homogenization with oscillating Dirichlet data
• Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization

Related

• Lectures on Periodic Homogenization of Elliptic Systems
• Boundary Layers in Periodic Homogenization of Neumann Problems
• L^p Neumann Problems in Homogenization of General Elliptic Systems
• Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization
• Homogenization of Elliptic Systems with Neumann Boundary Conditions