数学物理学报 ›› 2016, Vol. 36 ›› Issue (3): 481-492.

• 论文 • 上一篇    下一篇

Laplace方程斜边值问题的梯度估计

向妮1, 石菊花1, 徐金菊2, 吴燕1   

  1. 1 湖北大学数学与统计学学院应用数学湖北省重点实验室 武汉 430062;
    2 上海大学数学系 上海 200444
  • 收稿日期:2015-09-14 修回日期:2016-03-14 出版日期:2016-06-26 发布日期:2016-06-26
  • 作者简介:向妮,nixiang@hubu.edu.cn;石菊花,ashijuhua@163.com;徐金菊,jjxujane@shu.edu.cn;吴燕,18827363287@163.com
  • 基金资助:

    基金项目:国家自然科学基金(11101132)湖北省教育厅科学技术研究项目(Q20120105)和创新思维导向的微分方程课程开放式实践教学体系的研究项目资助

The Gradient Estimates of Laplace Equations with Oblique Boundary Value Problem

Xiang Ni1, Shi Juhua1, Xu Jinju2, Wu Yan1   

  1. 1 Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062;
    2 Department of Mathematics, Shanghai University, Shanghai 200444
  • Received:2015-09-14 Revised:2016-03-14 Online:2016-06-26 Published:2016-06-26
  • Supported by:

    Supported by the NSFC (11101132), the Foundation of Hubei Provincial Department of Education (Q20120105) and the Opening Practicle Teaching System Study for the Partial Differential Equations of Innovative Thinking Guide

摘要:

该文介绍了Laplace方程斜边值问题解的梯度估计的两种证明方法:第一种证明重新整理文献[1]中的梯度估计;第二种证明采用不同于文献[1]的辅助函数得到估计. 两种方法都充分利用函数在极大值点的性质,得到边界梯度估计和近边梯度估计,结合文献[2]中已有的梯度内估计,从而得到解的全局梯度估计.

关键词: Laplace方程, 斜边值问题, 梯度估计

Abstract:

In this paper, the authors study two proofs for the gradient estimates of the Laplace equations with oblique boundary value condition. For the first proof, the gradient estimates of Lieberman[1] are rearranged; for the second proof, barrier function which is different from [1] is used to obtain the gradient estimates. They both use the property of the maximum value point, and get the near boundary gradient estimates and boundary gradient estimates, combining the given inner gradient estimates in [2], and then they obtain the global gradient estimates.

Key words: Laplace equations, Oblique boundary value problem, Gradient estimates

中图分类号: 

  • O175.2