Year: 2026
Type: preprint
Abstract: We construct a continuous function $u$ on the closed unit ball in $\mathbb{R}^4$ and a smooth autonomous Hamiltonian $H:\mathbb{R}^4\to[1,2]$ for which $u$ solves $H(Du)=c$ in the unit ball in the viscosity sense for every $c\in[1,2]$. This reveals a striking and distinctive pathology of viscosity solutions: a fixed function and a fixed Hamiltonian need not determine the right-hand side of the equation.
Source: arXiv (Cornell University)
Authors: Tran, Hung V., Yu, Yifeng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7220686339