English

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}
}