Boundary Layers in Periodic Homogenization of Neumann Problems

Abstract

This paper is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order oscillating boundary data. We identify the homogenized system and establish the sharp rate of convergence in $L^2$ in dimension three or higher. Sharp regularity estimates are also obtained for the homogenized boundary data in both Dirichlet and Neumann problems. The results are used to obtain a higher-order convergence rate for Neumann problems with non-oscillating data.

arXiv comment54 pages; minor revision of the first version

References in corpus (2)

• Convergence Rates in L^2 for Elliptic Homogenization Problems
• Quantitative analysis of boundary layers in periodic homogenization

Cited by in corpus (4)

• Quantitative analysis of boundary layers in periodic homogenization
• A Large-Scale Regularity Theory for Random Elliptic Operators on the Half-Space with Homogeneous Neumann Boundary Data
• Optimal Boundary Estimates for Stokes Systems in Homogenization Theory
• Homogenization and boundary layers in domains of finite type