二维Monge-Ampère型方程的Neumann问题

数学物理学报 ›› 2015, Vol. 35 ›› Issue (4): 794-802.

二维Monge-Ampère型方程的Neumann问题

向妮, 石菊花, 王玉娥

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

收稿日期:2013-09-15 修回日期:2015-03-15 出版日期:2015-08-25 发布日期:2015-08-25
作者简介:向妮, nixiang@hubu.edu.cn;石菊花, ashijuhua@163.com;王玉娥, wangyue12630@163.com
基金资助:
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开放式实践教学体系的研究项目(201523)资助

The Neumann Boundary Value Problems of Two Dimensional Monge-Ampère Equations

Xiang Ni, Shi Juhua, Wang Yu'e

Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062

Received:2013-09-15 Revised:2015-03-15 Online:2015-08-25 Published:2015-08-25

摘要/Abstract

摘要：

该文通过构造闸函数将整体约化到边界, 证明了二维Monge-Ampère型方程Neumann边值问题解的二阶导数估计, 进而得到该方程Neumann边值问题经典解的存在性以及正则性.

关键词: 二维Monge-Ampè, re型方程, Neumann边值条件, 二阶导数估计

Abstract:

In this paper, we prove the second order derivatives estimates of Monge-Ampère type equations with Neumann boundary condition, using the method of auxiliary function which reduce the global estimates to the boundary. Then, we obtain the existence and regularity of the classical solutions for the equations.

Key words: Two dimensional Monge-Ampè, re type equations, Neumann boundary condition, Second order derivatives estimates

中图分类号:

O175.25

向妮, 石菊花, 王玉娥. 二维Monge-Ampère型方程的Neumann问题[J]. 数学物理学报, 2015, 35(4): 794-802.

Xiang Ni, Shi Juhua, Wang Yu'e. The Neumann Boundary Value Problems of Two Dimensional Monge-Ampère Equations[J]. Acta mathematica scientia,Series A, 2015, 35(4): 794-802.

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