Sökning: "hyperconvex domain"

Visar resultat 1 - 5 av 7 avhandlingar innehållade orden hyperconvex domain.

  1. 1. 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

  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. The complex Monge-Ampére operator on bounded hyperconvex domains

    Författare :Per Åhag; Urban Cegrell; Norm Levenberg; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Complex Monge-Ampère operator; currents; Dirichlet problem; hyperconvex domain; Perron-Bremermann envelope; pluripotential theory; plurisubharmonic function; Mathematical statistics; Matematisk statistik; Mathematical Statistics; matematisk statistik;

    Sammanfattning : .... 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. 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