Phragm\`en-Lindel\"of type theorems for elliptic equations on infinite graphs
Analysis of PDEs
2024-06-26 v2
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.
Cite
@article{arxiv.2406.06505,
title = {Phragm\`en-Lindel\"of type theorems for elliptic equations on infinite graphs},
author = {Stefano Biagi and Fabio Punzo},
journal= {arXiv preprint arXiv:2406.06505},
year = {2024}
}