On the comparison principle for a nonlocal infinity Laplacian

DOI: 10.1515/acv-2025-0054 ISSN: 1864-8258

Frida Fejne

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.