Search for dissertations about: "hyperconvex domain"
Showing result 1 - 5 of 7 swedish dissertations containing the words hyperconvex domain.
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1. Regularity and boundary behavior of solutions to complex Monge–Ampère equations
Abstract : In the theory of holomorphic functions of one complex variable it is often useful to study subharmonic functions. The subharmonic can be described using the Laplace operator. When one studies holomorphic functions of several complex variables one should study the plurisubharmonic functions instead. READ MORE
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2. 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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3. The complex Monge-Ampére operator on bounded hyperconvex domains
Abstract : .... 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. 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