Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows

We prove a logarithmic convexity result for exponentially weighted L2-norms of solutions to electromagnetic Schrödinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle...

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Bibliographic Details
Published in:Journal of functional analysis 2013-05, Vol.264 (10), p.2386-2415
Main Authors: Barceló, J.A., Fanelli, L., Gutiérrez, S., Ruiz, A., Vilela, M.C.
Format: Article
Language:English
Subjects:
Carleman estimates
Electromagnetic potentials
Schrödinger equation
Uncertainty principle
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Summary:We prove a logarithmic convexity result for exponentially weighted L2-norms of solutions to electromagnetic Schrödinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2013.02.017