On the (non) existence of viscosity solutions of multi-time Hamilton-Jacobi equations

Abstract

We prove that the multi-time Hamilton-Jacobi equation in general cannot be solved in the viscosity sense, in the non-convex setting, even when the Hamiltonians are in involution.

We have revised the Appendix by slightly changing the statement (and the proof) of Proposition A.2 (Comparison Principle). We needed Proposition A.2 in this modified form to fill a gap in the proof of Theorem A.1. We have also introduced some simplifications in the proof of Proposition A.2

References in corpus (3)

• Viscosity solution of Hamilton-Jacobi equation by a limiting minmax method
• Weak KAM for commuting Hamiltonians
• Semi-concave singularities and the Hamilton-Jacobi equation

Cited by in corpus (4)

• Convergence of solutions for some degenerate discounted Hamilton--Jacobi equations
• Stochastic homogenization and effective Hamiltonians of HJ equations in one space dimension: The double-well case
• Viscosity solutions of divergence type PDEs associated to multitime hybrid games
• Non-existence of global characteristics for viscosity solutions