Sökning: "plurisubharmonic functions"

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

  1. 1. 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 :NATURAL SCIENCES; NATURVETENSKAP; 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

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

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

    Sammanfattning : 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. LÄS MER

  3. 3. The plurisubharmonic Mergelyan property

    Författare :Lisa Hed; Urban Cegrell; Anders Fällström; Per Åhag; Jan Wiegerinck; Umeå universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; 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

  4. 4. Approximation and Subextension of Negative Plurisubharmonic Functions

    Författare :Lisa Hed; Urban Cegrell; Frank Wikström; Umeå universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; 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

  5. 5. On the Extension and Wedge Product of Positive Currents

    Författare :Ahmad Khalid Al Abdulaali; Jan-Erik Björk; Hassine El Mir; Stockholms universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; Closed positive currents; plurisubharmonic currents; plurisubharmonic functions; pluripolar sets; k-convex functions; wedge product of currents; matematik; Mathematics;

    Sammanfattning : This dissertation is concerned with extensions and wedge products of positive currents. Our study can be considered as a generalization for classical works done earlier in this field. Paper I deals with the extension of positive currents across different types of sets. LÄS MER