# H\"older regularity of viscosity solutions of some fully nonlinear equations in the Heisenberg group

## TL;DR

This paper establishes the H"older continuity of viscosity solutions to certain degenerate fully nonlinear equations within the Heisenberg group, advancing understanding of regularity in sub-Riemannian geometries.

## Contribution

It proves H"older regularity for viscosity solutions of degenerate fully nonlinear equations in the Heisenberg group, a significant step in sub-Riemannian PDE analysis.

## Key findings

- Viscosity solutions are H"older continuous in the Heisenberg group.
- Regularity results apply to degenerate fully nonlinear equations.
- Advances the theory of PDEs in sub-Riemannian geometries.

## Abstract

In this paper we prove the H\"older regularity of bounded, uniformly continuous, viscosity solutions of some degenerate fully nonlinear equations in the Heisenberg group.