Moduli of Continuity for Viscosity Solutions on Manifolds

TL;DR

This paper extends the estimates of modulus of continuity for viscosity solutions of nonlinear evolution equations from Euclidean spaces to manifolds, broadening the scope of previous results for regular and viscosity solutions.

Contribution

It generalizes existing modulus of continuity estimates from Euclidean spaces to manifolds for viscosity solutions of nonlinear evolution equations.

Findings

Established modulus of continuity estimates on manifolds

Extended previous Euclidean space results to manifold settings

Bridged gap between regular and viscosity solutions on manifolds

Abstract

We establish the estimates of modulus of continuity for viscosity solutions of nonlinear evolution equations on manifolds, extending previous work of B. Andrews and J. Clutterbuck for regular solutions on manifolds \cite{AC3} and the first author's recent work for viscosity solutions in Euclidean spaces \cite{me1}.