Phragmèn-Lindelöf type theorems for elliptic equations on infinite graphs

2024/06/10 by Stefano Biagi, Biagi, Stefano, Fabio Punzo +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2406.06505

openalex publication_date 2024/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the validity of the Phragmèn-Lindelöf principle for a class of elliptic equations with a potential, posed on infinite graphs. Consequently, we get uniqueness, in the class of solutions satisfying a suitable growth condition at infinity. We suppose that the \it outer degree (or outer curvature) of the graph is bounded from above, and we allow the potential to go to zero at infinity in a controlled way. Finally, we discuss the optimality of the conditions on the potential and on the outer degree on special graphs.

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• Nonexistence results for the semilinear wave equation on graphs

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