# A comparison among various notions of viscosity solutions for Hamilton-Jacobi equations on networks

arXiv: https://arxiv.org/abs/1301.0194 · HTML: https://mlsanity.com/paper/1301.0194/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2013.

## Built on by (most cited first, 2 of 2)

- [Models for information propagation on graphs](https://mlsanity.com/paper/2201.07577/) (2022)
- [Planner-Admissible Graph-PDE Value Extensions for Sparse Goal-Conditioned Planning](https://mlsanity.com/paper/2605.19185/) (2026)

## Abstract (arXiv)

Three definitions of viscosity solutions for Hamilton-Jacobi equations on networks recently appeared in literature ([1,4,6]). Being motivated by various applications, they appear to be considerably different. Aim of this note is to establish their equivalence.