Sökning: "plurisubharmonic functions"

Visar resultat 1 - 5 av 14 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 :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

3. 2. Boundary singularities of plurisubharmonic functions

   Författare :Mårten Nilsson; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; pluripotential theory; envelope of plurisubharmonic functions; complex Monge-Ampère equation; Jensen measures;

   Sammanfattning : We study the Perron–Bremermann envelope P(μ, φ):=sup{u(z) ; u ∈ PSH(Ω), (ddcu)n≥ μ, u^* ≤ φ} on a B-regular domain Ω. Such envelopes occupy a central position within pluripotential theory as they, for suitable μ and φ harmonic and continuous on the closure of Ω, constitute unique solutions to the Dirichlet problem for the complex Monge–Ampère operator. LÄS MER

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

   Författare :Berit Kemppe; Urban Cegrell; Anders Fällström; Alexander Raskovskii; Umeå universitet; []
   Nyckelord :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

5. 4. 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

7. 5. 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