Sökning: "plurisubharmonic function"

Visar resultat 1 - 5 av 13 avhandlingar innehållade orden plurisubharmonic function.

1. 1. The plurisubharmonic Mergelyan property

   Författare :Lisa Hed; Urban Cegrell; Anders Fällström; Per Åhag; Jan Wiegerinck; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Complex Monge-Ampère operator; approximation; plurisubharmonic function; subextension; Mergelyan property; plurisubharmonic function on compact sets; Jensen measures; Mathematics; matematik;

   Sammanfattning : In this thesis, we study two different kinds of approximation of plurisubharmonic functions. The first one is a Mergelyan type approximation for plurisubharmonic functions. LÄS MER

3. 2. Studies of the Boundary Behaviour of Functions Related to Partial Differential Equations and Several Complex Variables

   Författare :Håkan Persson; Kaj Nyström; Maciej Klimek; Evgeny Poletsky; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; uniformly parabolic equations; non-linear parabolic equations; linear growth; Lipschitz domain; NTA-domain; Riesz measure; boundary behavior; boundary Harnack; degenerate parabolic; parabolic measure; plurisubharmonic functions; continuous boundary; hyperconvexity; bounded exhaustion function; Hölder for all exponents; log-lipschitz; boundary regularity; approximation; Mergelyan type approximation; plurisubharmonic functions on compacts; Jensen measures; monotone convergence; plurisubharmonic extension; plurisubharmonic boundary values; Mathematics; Matematik;

   Sammanfattning : 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. LÄS MER

4. 3. Algebras of bounded holomorphic functions

   Författare :Anders Fällström; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; holomorphic function; bounded holomorphic function; domain of holomorphy; envelope of holomorphy; Gleason’s problem; convex set; uniform algebra; spectrum; fibers; generalized Shilov boundary; analytic structure; plurisubharmonic function;

   Sammanfattning : Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. LÄS MER

5. 4. Approximation and Subextension of Negative Plurisubharmonic Functions

   Författare :Lisa Hed; Urban Cegrell; Frank Wikström; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Complex Monge-Ampère operator; Approximation; Plurisubharmonic function; Subextension; MATHEMATICS; MATEMATIK;

   Sammanfattning : 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. LÄS MER

7. 5. Regularity and boundary behavior of solutions to complex Monge–Ampère equations

   Författare :Björn Ivarsson; Zbigniew Blocki; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Complex Monge--Ampère operator; interior regularity; plurisubharmonic function; blow-up rate of solutions; bounded plurisubharmonic exhaustion function; globally Lipschitz; strongly pseudoconvex domain; hyperconvex domain; Bergman kernel; MATEMATIK; MATHEMATICS; MATEMATIK; matematik; Mathematics;

   Sammanfattning : 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. LÄS MER