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 equatio...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.展开更多
The smooth solutions of the Dirichlet problems for the complex Monge-Ampère equations on general smooth domains are found,provided that there exists a C 3 strictly plurisub harmonic subsolution with prescribed b...The smooth solutions of the Dirichlet problems for the complex Monge-Ampère equations on general smooth domains are found,provided that there exists a C 3 strictly plurisub harmonic subsolution with prescribed boundary value.It is the smooth version of an existence theorem given by Bedford and Taylor.展开更多
基金supported by the Research Foundation of Beijing Government(Grant No.YB20081002802)National Natural Science Foundation of China(Grant No.10771144)
文摘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.
基金National Natural Science Foundation of China(1 0 0 71 0 70 ) and Foundation of Zhejiang Education Counci
文摘The smooth solutions of the Dirichlet problems for the complex Monge-Ampère equations on general smooth domains are found,provided that there exists a C 3 strictly plurisub harmonic subsolution with prescribed boundary value.It is the smooth version of an existence theorem given by Bedford and Taylor.
