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

Victor Issa

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arXiv · 2402.07665

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

Victor Issa

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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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Victor Issa. 2024-02-12. Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations. https://arxiv.org/abs/2402.07665

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