Work

Uniqueness of semi-concave weak Solutions for Hamilton–Jacobi Equations

Year: 2025

Type: article

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.

Source: Annales de la faculté des sciences de Toulouse Mathématiques

DOI: 10.5802/afst.1825

Author: Victor Issa

Institutions: École Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4391799294

FWCI: 1.886

Cites: 16

Cited by: 1

Related to: 10