scholarly journals On the generalized Dirichlet problem for plurisubharmonic functions

1964 ◽  
Vol 4 (1) ◽  
pp. 123-147 ◽  
Author(s):  
Yukio Kusunoki
Keyword(s):  
Dirichlet Problem ◽  
Plurisubharmonic Functions ◽  
Generalized Dirichlet

scholarly journals The Dirichlet Problem on the Upper Half-Space

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Jinjin Huang ◽  
Lei Qiao
Keyword(s):  
Dirichlet Problem ◽  
Half Space ◽  
Boundary Function ◽  
Dirichlet Integral ◽  
Fast Growing ◽  
Continuous Boundary ◽  
Generalized Dirichlet

A solution of the Dirichlet problem on the upper half-space is constructed by the generalized Dirichlet integral with a fast-growing continuous boundary function.

scholarly journals On Dirichlet's principle and problem

2012 ◽  
Vol 110 (2) ◽  
pp. 235 ◽  
Author(s):  
Per Åhag ◽  
Urban Cegrell ◽  
Rafal Czyz
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Complete Characterization ◽  
Plurisubharmonic Functions ◽  
Monge Ampere

The aim of this paper is to give a new proof of the complete characterization of measures for which there exists a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite pluricomplex energy. The proof uses variational methods.

THE DIRICHLET PROBLEM FOR MAXIMAL PLURISUBHARMONIC FUNCTIONS ON ANALYTIC VARIETIES IN ℂn

2009 ◽  
Vol 20 (04) ◽  
pp. 521-528 ◽  
Author(s):  
FRANK WIKSTRÖM
Keyword(s):  
Dirichlet Problem ◽  
Continuous Function ◽  
Plurisubharmonic Function ◽  
Boundary Values ◽  
Regular Domain ◽  
Analytic Variety ◽  
Plurisubharmonic Functions ◽  
Analytic Varieties

Let Ω be a B-regular domain in ℂn and let V be a locally irreducible analytic variety in Ω. Given a continuous function [Formula: see text], we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by ϕ and furthermore that u is continuous on [Formula: see text].

scholarly journals Quasibounded plurisubharmonic functions

2021 ◽  
pp. 2150068
Author(s):  
Mårten Nilsson ◽  
Frank Wikström
Keyword(s):  
Harmonic Functions ◽  
Boundary Data ◽  
Dirichlet Problems ◽  
Plurisubharmonic Functions ◽  
Pluripolar Set ◽  
Jensen Measures ◽  
Generalized Dirichlet

We extend the notion of quasibounded harmonic functions to the plurisubharmonic setting. As an application, using the theory of Jensen measures, we show that certain generalized Dirichlet problems with unbounded boundary data admit unique solutions, and that these solutions are continuous outside a pluripolar set.

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