The comparison principle and Dirichlet problem in the class , p > 0
We establish the comparison principle in the class . The result obtained is applied to the Dirichlet problem in .
The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ
We prove some existence results for the complex Monge-Ampère equation in ℂⁿ in a certain class of homogeneous functions in ℂⁿ, i.e. we show that for some nonnegative complex homogeneous functions g there exists a plurisubharmonic complex homogeneous solution u of the complex Monge-Ampère equation.
The complex Monge-Ampère operator in hyperconvex domains
The complex Monge-Ampère operator in the Cegrell classes [Book]
The general definition of the complex Monge-Ampère operator
We define and study the domain of definition for the complex Monge-Ampère operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain " test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.
The restriction theorem for fully nonlinear subequations
Let be a submanifold of a manifold . We address the question: When do viscosity subsolutions of a fully nonlinear PDE on , restrict to be viscosity subsolutions of the restricted subequation on ? This is not always true, and conditions are required. We first prove a basic result which, in theory, can be applied to any subequation. Then two definitive results are obtained. The first applies to any “geometrically defined” subequation, and the second to any subequation which can be transformed...
The symmetric pluricomplex Green function