关于多时 Hamilton-Jacobi 方程粘性解的（非）存在性
偏微分方程分析
2023-04-06 v2 辛几何
摘要
我们证明了在非凸设定下，即使 Hamilton 量处于对合状态，多时 Hamilton-Jacobi 方程通常也无法在粘性意义下求解。
引用
@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}
}
备注
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