On regularization of plurisubharmonic functions near boundary points

TL;DR

This paper demonstrates that all plurisubharmonic functions on Lipschitz domains in complex space can be smoothly approximated near boundary points, using an elementary proof method.

Contribution

It provides a simple, elementary proof that regularizes plurisubharmonic functions near boundary points of Lipschitz domains.

Findings

Regularization of plurisubharmonic functions near boundary points.

Elementary proof technique for boundary regularization.

Applicability to Lipschitz domains in complex analysis.

Abstract

We prove in an elementary way that for a Lipschitz domain $D\subset \cn$, all plurisubharmonic functions on $D$ can be regularized near any boundary point.