Uniqueness of solutions to elliptic and parabolic equations on metric graphs

2025/03/04 by Meglioli, Giulia, Punzo, Fabio · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.02551

Abstract

We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schrödinger 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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