We extend in a nonlinear context previous results obtained in [8], [9], [10]. In particular we present a precised version of Morawetz type estimates and a uniqueness criterion for solutions to subcritical NLS.
@article{BUMI_2008_9_1_3_791_0,
author = {Luis Vega and Nicola Visciglia},
title = {A Uniqueness Result for Solutions to Subcritical NLS},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {1},
year = {2008},
pages = {791-803},
zbl = {1191.35259},
mrnumber = {2455345},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_3_791_0}
}
Vega, Luis; Visciglia, Nicola. A Uniqueness Result for Solutions to Subcritical NLS. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 791-803. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_3_791_0/
[1] - - , Some dispersive estimates for Schrödinger equations with repulsive potentials, J. Funct. Anal., vol. 236 (2006), 1-24. | MR 2227127 | Zbl 1293.35090
[2] , Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics, vol. 10, New York University Courant Institute of Mathematical Sciences, New York, 2003. | MR 2002047
[3] - , Local smoothing properties of dispersive equations, J. Amer. Math. Soc., vol. 1 (1988), 413-439. | MR 928265 | Zbl 0667.35061
[4] - , Endpoint Strichartz estimates, Amer. J. Math., vol. 120 (1998), 955-980. | MR 1646048 | Zbl 0922.35028
[5] - , Lemmes de moments, de moyenne et de dispersion, C.R.A.S., vol. 314 (1992), 801-806. | MR 1166050 | Zbl 0761.35085
[6] , Regularity of solutions to the Schrödinger equation, Duke Math. J., vol. 55 (1987), 699-715. | MR 904948 | Zbl 0631.42010
[7] , Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc., vol. 102 (1988), 874-878. | MR 934859 | Zbl 0654.42014
[8] - , On the local smoothing for the free Schrödinger equation. Proc. Amer. Math. Soc., vol. 135 (2007), 119-128. | MR 2280200 | Zbl 1173.35107
[9] - , On the local smmothing for a class of conformally invariant Schrödinger equations. Indiana Univ. Math. J., vol. 56 (2007), 2265-2304. | MR 2360610 | Zbl 1171.35117
[10] - , Asymptotic lower bounds for a class of Schroedinger equations. Comm. Math. Phys., vol. 279 (2008), 429-453. | MR 2383594 | Zbl 1155.35098