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The comparison principle and Dirichlet problem in the class $_{p} (f)$ , p > 0

Pham Hoang Hiep (2006)

Annales Polonici Mathematici

We establish the comparison principle in the class $_{p} (f)$ . The result obtained is applied to the Dirichlet problem in $_{p} (f)$ .

The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ

Rafał Czyż (2001)

Annales Polonici Mathematici

We prove some existence results for the complex Monge-Ampère equation $(d d^{c} u) ⁿ = g d λ$ 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

Zbigniew Błocki (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The complex Monge-Ampère operator in the Cegrell classes [Book]

Rafał Czyż (2009)

The general definition of the complex Monge-Ampère operator

Urban Cegrell (2004)

Annales de l’institut Fourier

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

F. Reese Harvey, H. Blaine Lawson (2014)

Annales de l’institut Fourier

Let $X$ be a submanifold of a manifold $Z$ . We address the question: When do viscosity subsolutions of a fully nonlinear PDE on $Z$ , restrict to be viscosity subsolutions of the restricted subequation on $X$ ? 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

Urban Cegrell (1995)

Banach Center Publications