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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cutoff resolvent estimates and the semilinear Schrödinger equation


Author: Hans Christianson
Journal: Proc. Amer. Math. Soc. 136 (2008), 3513-3520
MSC (2000): Primary 35Q55
Published electronically: June 10, 2008
MathSciNet review: 2415035
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Abstract: This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schrödinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply well-known techniques to obtain well-posedness results for the semi-linear Schrödinger equation.


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Additional Information

Hans Christianson
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email: hans@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09290-3
PII: S 0002-9939(08)09290-3
Received by editor(s): June 29, 2007
Published electronically: June 10, 2008
Additional Notes: This research was partially conducted during the period the author was employed by the Clay Mathematics Institute as a Liftoff Fellow.
Communicated by: Hart F. Smith
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.