Cutoff resolvent estimates and the semilinear Schrödinger equation

Author:
Hans Christianson

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3513-3520

MSC (2000):
Primary 35Q55

DOI:
https://doi.org/10.1090/S0002-9939-08-09290-3

Published electronically:
June 10, 2008

MathSciNet review:
2415035

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-08-09290-3

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.