A remark on the H\"older regularity of solutions to the complex Hessian equation

TL;DR

This paper proves that the Dirichlet problem for the complex Hessian equation admits a H"older continuous solution if a subsolution with this property exists, removing previous assumptions about measure mass.

Contribution

It establishes H"older regularity of solutions under broader conditions by removing the finite total mass assumption on the measure.

Findings

H"older continuous solutions exist under new conditions

Removal of the finite mass assumption on the measure

Extension of previous regularity results

Abstract

We prove that the Dirichlet problem for the complex Hessian equation has the H\"older continuous solution provided it has a subsolution with this property. Compared to the previous result of Benali-Zeriahi and Charabati-Zeriahi we remove the assumption on the finite total mass of the measure on the right hand side.