The Parabolic Infinite-Laplace Equation in Carnot groups

TL;DR

This paper establishes the existence and uniqueness of viscosity solutions for a class of parabolic equations modeled on the infinite Laplace equation within Carnot groups, analyzing their stability and long-term behavior.

Contribution

It introduces a Carnot group framework for the parabolic infinite Laplace equation and proves key properties like existence, uniqueness, and stability of solutions.

Findings

Existence and uniqueness of viscosity solutions in Carnot groups.

Stability of solutions over time.

Asymptotic behavior as time approaches infinity.

Abstract

By employing a Carnot parabolic maximum principle, we show existence-uniqueness of viscosity solutions to a class of equations modeled on the parabolic infinite Laplace equation in Carnot groups. We show stability of solutions within the class and examine the limit as t goes to infinity.