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 $f\le 0$. Uniqueness is established through a comparison principle.

18 pages. To appear in Advances in Calculus of Variations