Search for dissertations about: "plurisubharmonic boundary values"
Found 5 swedish dissertations containing the words plurisubharmonic boundary values.
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1. Studies of the Boundary Behaviour of Functions Related to Partial Differential Equations and Several Complex Variables
Abstract : This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables.Paper I concerns solutions to non-linear parabolic equations of linear growth. READ MORE
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2. Boundary values of plurisubharmonic functions and related topics
Abstract : This thesis consists of three papers concerning problems related to plurisubharmonic functions on bounded hyperconvex domains, in particular boundary values of such functions. The papers summarized in this thesis are:* Paper I Urban Cegrell and Berit Kemppe, Monge-Ampère boundary measures, Ann. Polon. Math. READ MORE
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3. The plurisubharmonic Mergelyan property
Abstract : In this thesis, we study two different kinds of approximation of plurisubharmonic functions. The first one is a Mergelyan type approximation for plurisubharmonic functions. READ MORE
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4. Approximation and Subextension of Negative Plurisubharmonic Functions
Abstract : In this thesis we study approximation of negative plurisubharmonic functions by functions defined on strictly larger domains. We show that, under certain conditions, every function u that is defined on a bounded hyperconvex domain Ω in Cn and has essentially boundary values zero and bounded Monge-Ampère mass, can be approximated by an increasing sequence of functions {uj} that are defined on strictly larger domains, has boundary values zero and bounded Monge-Ampère mass. READ MORE
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5. Dirichlet's problem in Pluripotential Theory
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. READ MORE