Homogenization of elliptic systems with Neumann boundary conditions

Kenig, Carlos; Lin, Fanghua; Shen, Zhongwei

doi:10.1090/S0894-0347-2013-00769-9

Homogenization of elliptic systems with Neumann boundary conditions
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by Carlos E. Kenig, Fanghua Lin and Zhongwei Shen

J. Amer. Math. Soc. 26 (2013), 901-937

DOI: https://doi.org/10.1090/S0894-0347-2013-00769-9

Published electronically: March 27, 2013

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Abstract:

For a family of second-order elliptic systems with rapidly oscillating periodic coefficients in a $C^{1,\alpha }$ domain, we establish uniform $W^{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates on solutions with Neumann boundary conditions.

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