A class of Hamilton-Jacobi equations on Banach-Finsler manifolds

TL;DR

This paper investigates Hamilton-Jacobi equations on Banach-Finsler manifolds, focusing on subdifferentiability and establishing existence and uniqueness of viscosity solutions in this geometric setting.

Contribution

It introduces a framework for Hamilton-Jacobi equations on Banach-Finsler manifolds and proves key results on viscosity solutions' existence and uniqueness.

Findings

Established existence of viscosity solutions

Proved uniqueness of solutions under certain conditions

Extended Hamilton-Jacobi theory to Finsler manifold context

Abstract

The concept of subdifferentiability is studied in the context of $C^1$ Finsler manifolds (modeled on a Banach space with a Lipschitz $C^1$ bump function). A class of Hamilton-Jacobi equations defined on $C^1$ Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained.