On uniqueness sets of additive eigenvalue problems and applications

TL;DR

This paper introduces a PDE-based method to identify uniqueness sets in additive eigenvalue problems for Hamilton-Jacobi equations, with applications to understanding long-term behavior of solutions.

Contribution

It presents a novel, straightforward PDE approach for determining uniqueness sets in additive eigenvalue problems, enhancing analysis of Hamilton-Jacobi equations.

Findings

Provided a simple PDE method for uniqueness sets

Applied to large time behavior of Hamilton-Jacobi equations

Identified limiting profiles for solutions

Abstract

In this paper, we provide a simple way to find uniqueness sets for additive eigenvalue problems of first and second order Hamilton--Jacobi equations by using a PDE approach. An application in finding the limiting profiles for large time behaviors of first order Hamilton--Jacobi equations is also obtained.