Continuous solutions of Dirichlet problem to Hessian type equations for $(\omega,m)-\beta$-subharmonic functions on a ball in $\mathbb{C}^n$

TL;DR

This paper studies the continuity of solutions to the Dirichlet problem for complex Hessian-type equations involving $(eta,m)$-subharmonic functions on a complex ball, extending understanding of such equations in several complex variables.

Contribution

It establishes conditions for the continuity of solutions to Hessian-type equations for a specific class of subharmonic functions in complex analysis.

Findings

Proves continuity of solutions under certain boundary conditions.

Extends previous results to $(eta,m)$-subharmonic functions.

Provides new insights into complex Hessian equations on complex balls.

Abstract

In this paper, we investigate the continuity of solutions to the Dirichlet problem for complex Hessian-type equations associated with $(\omega, m)-\beta$-subharmonic functions on a ball in $\mathbb{C}^n$, where $ \beta=d d^c\|z\|^2=\frac{i}{2} \sum_{j=1}^n d z_j \wedge d \bar{z}_j $ is denoted the flat metric on $\mathbb{C}^n$.