Quasibounded plurisubharmonic functions

TL;DR

This paper extends quasibounded harmonic functions to plurisubharmonic functions, demonstrating existence and uniqueness of solutions to generalized Dirichlet problems with unbounded data, which are continuous outside a pluripolar set.

Contribution

It introduces a new class of quasibounded plurisubharmonic functions and applies Jensen measure theory to solve unbounded boundary value problems.

Findings

Existence of solutions to generalized Dirichlet problems with unbounded data.

Uniqueness of these solutions under the new framework.

Solutions are continuous outside a pluripolar set.

Abstract

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.