# The Dirichlet problem for $m$-subharmonic functions on compact sets

## TL;DR

This paper characterizes compact sets where the Dirichlet problem for continuous and m-harmonic m-subharmonic functions has solutions, advancing understanding in potential theory on compact sets.

## Contribution

It provides a characterization of compact sets that admit solutions to the Dirichlet problem for m-subharmonic functions, extending classical potential theory.

## Key findings

- Identifies conditions on compact sets for solvability of the Dirichlet problem.
- Establishes existence of solutions within classes of continuous and m-harmonic m-subharmonic functions.
- Enhances understanding of boundary value problems in complex potential theory.

## Abstract

We characterize those compact sets for which the Dirichlet problem has a solution within the class of continuous $m$-subharmonic functions defined on a compact set, and then within the class of $m$-harmonic functions.