OnthesolutionofDirichlet’sproblemofcomplexMonge-Amp`ereequationonCartan-Hartogsdomainofthesecondtype资源-CSDN文库

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On the solution of Dirichlet’s problem of

complex Monge-Amp`ere equation on

Cartan-Hartogs domain of the second type*

1

Weiping YIN

1

Xiaolan YIN

2,3

1. School of Mathematical Sciences, Capital Normal University, Beijing

100037, China. e-mail: wyin@mail.cnu.edu.cn Tel: 86-10-68902600

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.

Abstract: Complex Monge-Amp`ere equation is a nonlinear equation with

high degree, therefore to get its solution is very diﬃcult. In present paper how

to get the solution of Dirichlet’s problem of Complex Monge-Amp`ere equation

on the Cartan-Hartogs domain of the second type is discussed by using the

analytic method. Firstly, the complex Monge-Amp`ere equation is reduced to

the nonlinear ordinary diﬀerential equation, then the solution of the Dirichlet’s

problem of complex Monge-Amp`ere equation is reduced to the solution of two

point boundary value problem of the nonlinear second-order ordinary diﬀer-

ential equation. Secondly, the solution of the Dirichlet’s problem is given in

semi-explicit formula, and under the special case the exact solution is obtained.

These results may be helpful for the numerical method of Dirichlet’s problem

of complex Monge-Amp`ere equation on the Cartan-Hartogs domain.

Key Words Complex Monge-Amp`ere equation, Dirichlet’s problem,

Cartan-Hartogs domain, Kaehler-Einstein metric.

MR(1991)Subject Classiﬁcation: 65E05, 32C17, 53C55, 35G30.

1

*This project was supported by the National Natural Science Foundation of China(Grant

No.10771144).

1

http://www.paper.edu.cn

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