On the comparison principle for a nonlocal infinity Laplacian

Abstract

In this article, we prove the uniqueness of viscosity solutions to $\mathcal{L}_{\infty} u =f$ in $\Omega$, where $\mathcal{L}_{\infty}$ denotes the nonlocal infinity Laplace operator, $\Omega$ a bounded domain, and $f$ a continuous functions such that $f \leq 0$. Uniqueness is established through a comparison principle.