Search for dissertations about: "PLURISUBHARMONIC-FUNCTIONS"

Showing result 1 - 5 of 11 swedish dissertations containing the word PLURISUBHARMONIC-FUNCTIONS.

2. 1. Boundary singularities of plurisubharmonic functions

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

   Abstract : 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. 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. 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

6. 4. 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

7. 5. Convexity, Currents, and Lelong numbers

   Author : Aron Lagerberg; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; complex analysis; convex analysis; currents; Lelong numbers; tropical geometry; L^2-estaimtes; Legendre transform; intersection theory; real Monge-Ampere operators; plurisubharmonic functions; integrability index; L^2-estaimtes;

   Abstract : This thesis treats different aspects of convexity, both real and complex. On the real side, we study convexity in relation with certain currents. On the complex side, we study the singularities of plurisubharmonic functions. READ MORE