Dirichlet's problem in Pluripotential Theory

University dissertation from Umeå : Matematik och matematisk statistik

Author: Hoàng Hiệp Phạm; Umeå Universitet.; [2008]

Keywords: NATURVETENSKAP; NATURAL SCIENCES; Complex Monge-Ampère operator; currents; Dirichlet problem; pluripotential theory; plurisubharmonic function; subextension; MATHEMATICS; MATEMATIK;

Abstract: In this thesis we focus on Dirichlet's problem for the complex Monge-Ampère equation. That is, for a given non-negative Radon measure µ we are interested in the conditions under which there exists a plurisubharmonic function u such that (ddcu)n=µ, where (ddc)n is the complex Monge-Ampère operator. If this function u exists, then can it be chosen with given boundary values? Is this solution uniquely determined within a given class of functions?

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