Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations
Analysis of PDEs
2024-02-16 v2
Abstract
It is well known that when the nonlinearity is convex, the Hamilton-Jacobi PDE admits a unique semi-convex weak solution, which is the viscosity solution. In this paper, motivated by problems arising from spin glasses, we show that if the Hamilton-Jacobi PDE with strictly convex nonlinearity and regular enough initial condition admits a semi-concave weak solution, then this solution is the viscosity solution.
Keywords
Cite
@article{arxiv.2402.07665,
title = {Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations},
author = {Victor Issa},
journal= {arXiv preprint arXiv:2402.07665},
year = {2024}
}