On the comparison principle for a nonlocal infinity Laplacian

Abstract

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