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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle


Author: Jason L. Metcalfe
Journal: Trans. Amer. Math. Soc. 356 (2004), 4839-4855
MSC (2000): Primary 35L05
Published electronically: June 25, 2004
MathSciNet review: 2084401
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Abstract: In this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done previously by H. Smith and C. Sogge in odd spatial dimensions. In order to prove the global estimates, we explore weighted Strichartz estimates for solutions of the wave equation when the Cauchy data and forcing term are compactly supported.


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Additional Information

Jason L. Metcalfe
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: metcalfe@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03667-0
PII: S 0002-9947(04)03667-0
Received by editor(s): November 14, 2002
Published electronically: June 25, 2004
Article copyright: © Copyright 2004 American Mathematical Society