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．
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.
出处
《数学年刊（A辑）》
CSCD
北大核心
2007年第3期347-358,共12页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10631020)资助的项目.
