Cutoff resolvent estimates and the semilinear Schrödinger equation
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- by Hans Christianson PDF
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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.References
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Additional Information
- Hans Christianson
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
- MR Author ID: 695231
- Email: hans@math.mit.edu
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3513-3520
- MSC (2000): Primary 35Q55
- DOI: https://doi.org/10.1090/S0002-9939-08-09290-3
- MathSciNet review: 2415035