# H\"{o}lder continuous solutions to quaternionic Monge-Amp\`{e}re equations

## TL;DR

This paper proves that solutions to quaternionic Monge-Ampère equations with certain density conditions are Hölder continuous on specific domains, advancing understanding of regularity in quaternionic analysis.

## Contribution

It establishes Hölder continuity of solutions to quaternionic Monge-Ampère equations with densities in L^p for p>2 on bounded strictly pseudoconvex domains.

## Key findings

- Solutions are Hölder continuous under given conditions
- Regularity results extend quaternionic Monge-Ampère theory
- Addresses equations with densities in L^p, p>2

## Abstract

We prove the H\"{o}lder continuity of the unique solution to quaternionic Monge-Amp\`{e}re equation with densities in $L^{p},$ $p>2,$ on a bounded strictly pseudoconvex domains.