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arXiv · 2406.06505

Phragm\`en-Lindel\"of type theorems for elliptic equations on infinite graphs

Stefano Biagi·Fabio Punzo
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Abstract

We investigate the validity of the Phragm\`en-Lindel\"of 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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Stefano Biagi, Fabio Punzo. 2024-06-10. Phragm\`en-Lindel\"of type theorems for elliptic equations on infinite graphs. https://arxiv.org/abs/2406.06505

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