H\"older continuous solutions to complex Hessian equations

TL;DR

This paper establishes the H"older continuity of solutions to complex Hessian equations with specific boundary and density conditions in pseudoconvex domains, extending regularity results in complex analysis.

Contribution

It proves H"older continuity for solutions to complex Hessian equations with right-hand side in L^p, under boundary and density conditions, for the first time in this setting.

Findings

Solutions are H"older continuous under given conditions

Regularity depends on boundary data and density near boundary

Results extend previous regularity theories in complex Hessian equations

Abstract

We prove the H\"older continuity of the solution to complex Hessian equation with the right hand side in $L^p$, $p>\frac{n}{m}$, $1< m< n$, in a $m$-strongly pseudoconvex domain in $\mathbb{C}^n$ under some additional conditions on the density near the boundary and on the boundary data.