Approximation and Bounded Plurisubharmonic Exhaustion Functions Beyond Lipschitz Domains

TL;DR

This paper extends the theory of plurisubharmonic functions and exhaustion functions to domains with less regular boundaries, using PDE techniques to analyze boundary behavior beyond Lipschitz regularity.

Contribution

It introduces methods to construct approximation and exhaustion functions on less regular domains, surpassing previous Lipschitz boundary limitations.

Findings

Extended plurisubharmonic approximation results

Constructed bounded plurisubharmonic exhaustion functions

Applied PDE techniques to low-regularity boundary analysis

Abstract

Using techniques from the analysis of PDEs to study the boundary behaviour of functions on domains with low boundary regularity, we extend results by Forna\ae{}ss-Wiegerinck (1989) on plurisubharmonic approximation and by Demailly (1987) on the existence on bounded plurisubharmonic exhaustion functions to domains beyond Lipschitz boundary regularity.