Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Cutoff resolvent estimates and the semilinear Schrödinger equation
HTML articles powered by AMS MathViewer

by Hans Christianson PDF
Proc. Amer. Math. Soc. 136 (2008), 3513-3520 Request permission

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35Q55
  • Retrieve articles in all journals with MSC (2000): 35Q55
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