NLS ground states on metric trees: existence results and open questions
Simone Dovetta, Politecnico di Torino
Sala conferenze IMATI-CNR, Pavia – Martedì 8 Ottobre 2019 h.15:00
Abstract. The talk discusses the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. After overviewing some known results for other types of metric graphs, we show that several new features appear on trees, such as the existence of minimizers with positive energy, and the emergence of unexpected threshold phenomena. The problem with a radial symmetry constraint is considered too, that is in principle different from the free problem due to the failure of the Pólya-Szegö inequality for radial rearrangements. This is a joint work with Enrico Serra and Paolo Tilli.