English

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}
}