An application of the Theorem on Sums to viscosity solutions of degenerate fully nonlinear equations

TL;DR

This paper establishes H"older continuity of viscosity solutions for degenerate fully nonlinear equations in ^n, including certain operators in Carnot groups, expanding the understanding of regularity in complex geometric contexts.

Contribution

It applies the Theorem on Sums to prove regularity of viscosity solutions for a broad class of degenerate nonlinear equations, including those in Carnot groups.

Findings

Viscosity solutions are Hf6lder continuous in ^n.

Results extend to some operators in Carnot groups.

Provides a new approach to regularity in degenerate nonlinear PDEs.

Abstract

We prove H\"older continuous regularity of bounded, uniformly continuous, viscosity solutions of degenerate fully nonlinear equations defined in all of $\mathbb{R}^n$ space. In particular the result applies also to some operators in Carnot groups.