Comparison Principles for nonlocal Hamilton-Jacobi equations

TL;DR

This paper establishes a comparison principle for viscosity solutions of degenerate nonlocal Hamilton-Jacobi equations with nonlinear gradient terms, applicable to equations of order 0<s<1.

Contribution

It provides a novel comparison principle for a broad class of nonlocal Hamilton-Jacobi equations with nonlinearities, extending existing theory.

Findings

Proves the comparison principle for viscosity solutions.

Applicable to equations of order 0<s<1.

Handles general nonlocal gradient nonlinearities.

Abstract

We prove the comparison principle for viscosity sub and super solutions of degenerate nonlocal operators with general nonlocal gradient nonlinearities. The proofs apply to purely Hamilton-Jacobi equations of order $0<s<1$.