Estimates for the $\infty$-Laplacian relative to vector fields

TL;DR

This paper establishes a H"older regularity estimate for viscosity solutions of inhomogeneous equations involving the infinity Laplace operator relative to a frame of vector fields, advancing understanding of their regularity properties.

Contribution

It introduces a novel regularity estimate for solutions of inhomogeneous infinity Laplace equations relative to vector fields, extending previous results to more general settings.

Findings

Proves H"older regularity for viscosity solutions

Extends regularity results to inhomogeneous equations

Provides new tools for analyzing infinity Laplace equations

Abstract

In this paper we prove a H\"older regularity estimate for viscosity solutions of inhomogeneous equations governed by the infinite Laplace operator relative to a frame of vector fields.