NLS ground states on metric trees: existence results and open questions

Dovetta, S.; Serra, E.; Tilli, P.

doi:10.1112/jlms.12361

We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence of minimizers with positive energy, and the emergence of unexpected threshold phenomena. We also study the problem with a radial symmetry constraint that is in principle different from the free problem due to the failure of the Pólya–Szegő inequality for radial rearrangements. A key role is played by a new Poincaré inequality with remainder.

NLS ground states on metric trees: existence results and open questions / Dovetta, S.; Serra, E.; Tilli, P.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 102:3(2020), pp. 1223-1240. [10.1112/jlms.12361]

Titolo:	NLS ground states on metric trees: existence results and open questions
Autori:	DOVETTA, SIMONE SERRA, Enrico TILLI, PAOLO
Data di pubblicazione:	2020
Rivista:	JOURNAL OF THE LONDON MATHEMATICAL SOCIETY
Digital Object Identifier (DOI):	http://dx.doi.org/10.1112/jlms.12361
Appare nelle tipologie:	1.1 Articolo in rivista

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