In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a fu...In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class E(Ω).展开更多
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
文摘In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class E(Ω).
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.
