Boundary Layers in Periodic Homogenization of Neumann Problems

Zhongwei Shen; Jinping Zhuge

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arXiv · 1610.05273

Boundary Layers in Periodic Homogenization of Neumann Problems

Zhongwei Shen·Jinping Zhuge

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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.

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Zhongwei Shen, Jinping Zhuge. 2016-10-26. Boundary Layers in Periodic Homogenization of Neumann Problems. https://arxiv.org/abs/1610.05273

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