Cutoff resolvent estimates and the semilinear Schrödinger equation
Author:
Hans Christianson
Journal:
Proc. Amer. Math. Soc. 136 (2008), 35133520
MSC (2000):
Primary 35Q55
Published electronically:
June 10, 2008
MathSciNet review:
2415035
Fulltext PDF Free Access
Abstract 
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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, nontrapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply wellknown techniques to obtain wellposedness results for the semilinear 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/S0002993908092903
PII:
S 00029939(08)092903
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.
