Jensen measures and boundary values of plurisubharmonic functions

In this paper, we study the approximation of negative plurisubharmonic functions with given boundary values. We want to approximate a plurisubharmonic function by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

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

International Journal of Mathematics ◽

10.1142/s0129167x09005376 ◽

2009 ◽

Vol 20 (04) ◽

pp. 521-528 ◽

Cited By ~ 2

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].

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Quasibounded plurisubharmonic functions

International Journal of Mathematics ◽

10.1142/s0129167x21500683 ◽

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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Convergence in capacity of plurisubharmonic functions with given boundary values

International Journal of Mathematics ◽

10.1142/s0129167x17500185 ◽

2017 ◽

Vol 28 (03) ◽

pp. 1750018 ◽

Cited By ~ 6

Author(s):

Nguyen Xuan Hong ◽

Nguyen Van Trao ◽

Tran Van Thuy

Keyword(s):

Boundary Values ◽

Plurisubharmonic Functions ◽

Monge Ampere ◽

Stability Results ◽

Convergence In Capacity

In this paper, we study the convergence in the capacity of sequence of plurisubharmonic functions. As an application, we prove stability results for solutions of the complex Monge–Ampère equations.

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