On the solution of Dirichlet problem of complex Monge-Ampère equation on Cartan-Hartogs domain of the second type  

作　　者：YIN WeiPing YIN XiaoLan 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 10048,China [2]Technology Center of Software Engineering,Institute of Software,Chinese Academy of Sciences,Beijing 100080,China [3]Graduate University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science China Mathematics》2009年第12期2829-2840,共12页中国科学：数学（英文版）

基　　金：supported by the Research Foundation of Beijing Government(Grant No.YB20081002802);National Natural Science Foundation of China(Grant No.10771144)

摘　　要：Complex Monge-Ampère equation is a nonlinear equation with high degree, so its solution is very difficult to get. How to get the plurisubharmonic solution of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method in this paper. Firstly, the complex Monge-Ampère equation is reduced to a nonlinear second-order ordinary differential equation (ODE) by using quite different method. Secondly, the solution of the Dirichlet problem is given in semi-explicit formula, and under a special case the exact solution is obtained. These results may be helpful for the numerical method of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain.Complex Monge-Ampère equation is a nonlinear equation with high degree,so its solution is very diffcult to get.How to get the plurisubharmonic solution of Dirichlet problem of complex Monge- Ampère equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method in this paper.Firstly,the complex Monge-Ampère equation is reduced to a nonlinear secondorder ordinary differential equation(ODE)by using quite different method.Secondly,the solution of the Dirichlet problem is given in semi-explicit formula,and under a special case the exact solution is obtained.These results may be helpful for the numerical method of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain.

关 键 词：complex Monge-Ampère equation Dirichlet problem Cartan-Hartogs domain Kaehler-Einstein metric 65E05 32C17 53C55 35G30 

分 类 号：O175[理学—数学]