A Curious Equation Involving the Infinity-Laplacian

TL;DR

This paper establishes the uniqueness of viscosity solutions for a differential equation involving the infinity-Laplacian with variable exponent and derives a version of Harnack's inequality for this problem.

Contribution

It introduces a novel uniqueness proof for solutions of the infinity-Laplacian with variable exponent and extends Harnack's inequality to this context.

Findings

Proved uniqueness of viscosity solutions.

Derived a version of Harnack's inequality.

Extended analysis to variable exponent cases.

Abstract

We prove the uniqueness for viscosity solutions of a differential equation involving the infinity-Laplacian with a variable exponent. A version of the Harnack's inequality is derived for this minimax problem.