H\"older continuous solutions to the complex Monge-Amp\`ere equations in non-smooth pseudoconvex domains

TL;DR

This paper establishes the H"older continuity of solutions to complex Monge-Ampère equations within non-smooth pseudoconvex domains, advancing understanding of regularity in complex analysis.

Contribution

It proves H"older continuity of solutions in non-smooth pseudoconvex domains, a significant extension beyond smooth domain cases.

Findings

Solutions are H"older continuous in non-smooth pseudoconvex domains.

Extends regularity results to less regular domains.

Provides new techniques for analyzing complex Monge-Ampère equations.

Abstract

In this paper, we prove the H\"older continuity for solutions to the complex Monge-Amp\`ere equations on non-smooth pseudoconvex domains of plurisubharmonic type ${m}$.