Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations

2024/02/12 by Issa, Victor · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.07665

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.

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