Uniqueness of solutions to elliptic and parabolic equations on metric graphs
Analysis of PDEs
2025-03-05 v1
Abstract
We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schr\"odinger equation with a potential, and the heat equation with a variable density. We assume suitable growth conditions on the solutions, which are related to the behaviour at infinity of the potential or of the density.
Keywords
Cite
@article{arxiv.2503.02551,
title = {Uniqueness of solutions to elliptic and parabolic equations on metric graphs},
author = {Giulia Meglioli and Fabio Punzo},
journal= {arXiv preprint arXiv:2503.02551},
year = {2025}
}