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arXiv · 2503.02551

Uniqueness of solutions to elliptic and parabolic equations on metric graphs

Giulia Meglioli·Fabio Punzo
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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.

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Giulia Meglioli, Fabio Punzo. 2025-03-04. Uniqueness of solutions to elliptic and parabolic equations on metric graphs. https://arxiv.org/abs/2503.02551

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