Neumann边值齐次化问题:W1, p强收敛估计

数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1115-1124.

Neumann边值齐次化问题:W^{1, p}强收敛估计

王娟*(),赵杰

中原工学院理学院郑州 451191

收稿日期:2018-11-23 出版日期:2019-10-26 发布日期:2019-11-08
通讯作者: 王娟 E-mail:wangjuan03022204@163.com
基金资助:
国家自然科学基金(11626239);河南省教育厅(18A110037);国家留学基金委(201708410483)

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)

摘要/Abstract

摘要：

该文研究了具有迅速振荡Neumann边值齐次化问题解的W^1，p收敛率.此类问题在齐次化的高阶逼近理论中有着很重要的作用，其往往被用来描述边界分层想象.该文主要用到了解的积分表示、振荡积分估计以及周期函数Fourier展开等核心思想和技术.

关键词: 齐次化, 收敛率, 振荡, Neumann函数

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

中图分类号:

O175.23

王娟,赵杰. Neumann边值齐次化问题:W^{1, p}强收敛估计[J]. 数学物理学报, 2019, 39(5): 1115-1124.

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.

参考文献 7

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