Search for dissertations about: "boundary values of plurisubharmonic functions"

Found 5 swedish dissertations containing the words boundary values of plurisubharmonic functions.

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

    Author : Håkan Persson; Kaj Nyström; Maciej Klimek; Evgeny Poletsky; Uppsala universitet; []
    Keywords : 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;

    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

  4. 2. Boundary values of plurisubharmonic functions and related topics

    Author : Berit Kemppe; Urban Cegrell; Anders Fällström; Alexander Raskovskii; Umeå universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Plurisubharmonic functions; boundary measures; boundary values; complex Monge-Ampère operator; weak*-convergence; Mathematical analysis; Analys; Mathematics; matematik;

    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

  5. 3. Approximation and Subextension of Negative Plurisubharmonic Functions

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

    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

  6. 4. The plurisubharmonic Mergelyan property

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

    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

  7. 5. Dirichlet's problem in Pluripotential Theory

    Author : Hoàng Hiệp Phạm; Urban Cegrell; Slawomir Kolodziej; Umeå universitet; []
    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. READ MORE