Homogenization of Elliptic Systems with Neumann Boundary Conditions

Carlos E. Kenig; Fanghua Lin; Zhongwei Shen

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arXiv · 1010.6114

Homogenization of Elliptic Systems with Neumann Boundary Conditions

Carlos E. Kenig·Fanghua Lin·Zhongwei Shen

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Abstract

The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators $\{\mathcal{L}_\varepsilon, \varepsilon>0\}$, arising in the theory of homogenization, with rapidly oscillating periodic coefficients. We establish sharp $W^{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates, which are uniform in the parameter $\varepsilon$, on solutions with Neumann boundary conditions in $C^{1,\alpha}$ domains.

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Carlos E. Kenig, Fanghua Lin, Zhongwei Shen. 2010-10-29. Homogenization of Elliptic Systems with Neumann Boundary Conditions. https://arxiv.org/abs/1010.6114

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