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一类Monge-Ampère方程的特征值问题
  • ISSN号：1000-8314
  • 期刊名称：《数学年刊：A辑》
  • 时间：0
  • 分类：O175.25[理学—数学;理学—基础数学]
  • 作者机构：[1]复旦大学数学科学学院,上海200433
  • 相关基金：国家自然科学基金（No.10631020）资助的项目.
作者： 王伟叶[1]
关键词： MONGE-AMPèRE方程, 特征值, 椭圆型方程, 移动平面法, Monge-Ampèreequation, Eigenvalue, Elliptic equation, Movingplane method
中文摘要：

对一类Monge-Ampère方程的特征值问题进行了研究．通过移动平面法证明了在凸对称区域内,Dirichlet问题的C^2凹（凸）解一定是对称的．进而通过对常微分方程和椭圆形偏微分方程的讨论,得到一类n维单位球上特征值问题的非平凡解的存在性和正则性结果．

英文摘要：

This paper mainly focuses on a kind of eigenvalue problems of the Monge-Ampère equation. By meas of the moving plane method in the study of second-order elliptic equation, the author proves that the symmetry of the convex domain to this problem implies the symmetry of every C^2 convex （or concave） solution to the Dirichlet problem. Through the study of an ODE linked to our main problem, the existence and regularity of the eigenvalue problem is also obtained.

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期刊信息
  • 《数学年刊：A辑》
  • 中国科技核心期刊
  • 主管单位:国家教育部
  • 主办单位:复旦大学
  • 主编：李大潜
  • 地址：上海市长乐路746号
  • 邮编：200040
  • 邮箱：edcam@fudan.edu.cn
  • 电话：021-65642338
  • 国际标准刊号：ISSN：1000-8314
  • 国内统一刊号：ISSN：31-1328/O1
  • 邮发代号:4-298
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:4264