English

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

Analysis of PDEs 2023-04-06 v2 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1312.1045,
  title  = {On the (non) existence of viscosity solutions of multi-time Hamilton-Jacobi equations},
  author = {Andrea Davini and Maxime Zavidovique},
  journal= {arXiv preprint arXiv:1312.1045},
  year   = {2023}
}

Comments

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