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Stampa

SEMINARI DI ANALISI MATEMATICA

Evento 

Titolo:
Existence and orbital stability of the ground states with prescribed \(L^2\) --norm for the NLS on bounded domains
Quando:
20.11.2013 14.40 h
Dove:
Palazzo Campana - Torino
Aula:
Aula C
Relatore:
Prof. Hugo Tavares
Afferenza:
Instituto Superior Técnico Universidade de Lisboa
Proponente:
S. Terracini
Locandina:
Locandina

Descrizione

Given \(\rho>0\), we are interested in the solutions \((U,\lambda)\in H^1_0(\Omega)\times \mathbb{R}\) of the elliptic problem $$ -\Delta U+\lambda U=U^p,\qquad \int_\Omega U^2\, =\rho,\quad U>0, $$ where \(\Omega\) is a bounded domain and \(p\) is Sobolev subcritical. We give conditions which ensure existence of solution, which turn out to be necessary and sufficient when \(\Omega\) is a ball. Moreover, if the domain is a ball, we show that standing waves associated to least energy solutions are orbitally stable for every \(\rho\) (in the existence range) when \(p\) is \(L^2\)--subcritical and critical, i.e., \(11+4/N\). This marks a substancial difference between the cases \(\Omega\) bounded and \(\Omega=\mathbb{R}^N\) The proofs are obtained in connection with the study of a variational problem with two constraints of independent interest (joint work with Benedetta Noris and Gianmaria Verzini).

Sede

Mappa
Sede:
Palazzo Campana   -   Sito web
Via:
Via Carlo Alberto, 10
Cap:
10123
Città:
Torino
Provincia:
To
Paese:
Paese: it

Descrizione

Dipartimento di Matematica, Università degli Studi di Torino

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