Neumann边值齐次化问题:W1, p强收敛估计

Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1115-1124.

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Homogenization of the Neumann Boundary Value Problem: The Sharper W^{1, p} Estimate

Juan Wang*(),Jie Zhao

College of Science, Zhongyuan University of Technology, Zhengzhou 451191

Received:2018-11-23 Online:2019-10-26 Published:2019-11-08
Contact: Juan Wang E-mail:wangjuan03022204@163.com
Supported by:
the NSFC(11626239);the Education Department of Henan Province(18A110037);the CSC(201708410483)

Abstract

Abstract:

In this paper, we shall strengthen our results on the W^{1, p} convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data. Such a problem raised due to its importance for higher order approximation in homogenization theory, which gives rise to the so-called boundary layer phenomenon. Our techniques are based on integral representation of the solutions as well as analysis of oscillatory integrals, in conjunction with Fourier expansion of the oscillating periodic function.

Key words: Homogenization, Convergence rates, Oscillating, Neumann functions

CLC Number:

O175.23

Juan Wang,Jie Zhao. Homogenization of the Neumann Boundary Value Problem: The Sharper W^{1, p} Estimate[J].Acta mathematica scientia,Series A, 2019, 39(5): 1115-1124.

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References 7

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Homogenization of the Neumann Boundary Value Problem: The Sharper W^{1, p} Estimate

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Homogenization of the Neumann Boundary Value Problem: The Sharper W^{1, p} Estimate