Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian

TL;DR

This paper investigates the Cauchy problem for the parabolic infinity Laplace equation, establishing a new comparison principle that ensures uniqueness of viscosity solutions with polynomial growth, extending prior linear growth results.

Contribution

It introduces a novel comparison principle for the parabolic infinity Laplace equation and proves uniqueness of solutions under polynomial growth conditions, improving previous linear growth assumptions.

Findings

Established a new comparison principle for the equation.

Proved uniqueness of viscosity solutions with polynomial growth.

Extended the class of functions for which uniqueness holds.

Abstract

We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous results obtained assuming a linear growth.