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In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
@article{ASNSP_2004_5_3_1_139_0,
author = {Banica, Valeria},
title = {Remarks on the blow-up for the {Schr\"odinger} equation with critical mass on a plane domain},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {139--170},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 3},
number = {1},
year = {2004},
mrnumber = {2064970},
zbl = {1170.35528},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_1_139_0/}
}
TY - JOUR AU - Banica, Valeria TI - Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 139 EP - 170 VL - 3 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_1_139_0/ LA - en ID - ASNSP_2004_5_3_1_139_0 ER -
%0 Journal Article %A Banica, Valeria %T Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 139-170 %V 3 %N 1 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_1_139_0/ %G en %F ASNSP_2004_5_3_1_139_0
Banica, Valeria. Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 1, pp. 139-170. http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_1_139_0/