Proceedings of the American Mathematical Society

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

   
 

 

Localized energy estimates for wave equations on high-dimensional Schwarzschild space-times


Authors: Parul Laul and Jason Metcalfe
Journal: Proc. Amer. Math. Soc. 140 (2012), 3247-3262
MSC (2010): Primary 35L05
Published electronically: January 31, 2012
MathSciNet review: 2917097
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Abstract: The localized energy estimate for the wave equation is known to be a fairly robust measure of dispersion. Recent analogs on the $ (1+3)$-dimensional Schwarzschild space-time have played a key role in a number of subsequent results, including a proof of Price's law. In this article, we explore similar localized energy estimates for wave equations on $ (1+n)$-dimensional hyperspherical Schwarzschild space-times.


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Additional Information

Parul Laul
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
Address at time of publication: DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
Email: p.laul@dpmms.cam.ac.uk

Jason Metcalfe
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11239-0
Received by editor(s): August 30, 2010
Received by editor(s) in revised form: January 13, 2011, and March 30, 2011
Published electronically: January 31, 2012
Additional Notes: The second author was supported in part by the NSF through grant DMS0800678.
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.