Stability for the Infinity-Laplace Equation with variable exponent

TL;DR

This paper investigates the stability of viscosity solutions to a variable exponent Infinity-Laplace equation, emphasizing the role of approximation techniques in establishing stability results.

Contribution

It introduces a stability analysis framework for the Infinity-Laplace equation with variable exponents, expanding understanding of solution behavior under perturbations.

Findings

Established stability results for viscosity solutions with variable exponents.

Highlighted the importance of approximation of the identity in proofs.

Extended classical stability results to more general variable exponent settings.

Abstract

The stability for the viscosity solutions of a differential equation with a perturbation term added to the Infinity-Laplace Operator is studied. This is the so-called Infinity-Laplace Equation with variable exponent infinity. An approximation of the identity is crucial for the proofs.