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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III


Author: Daniel Tataru
Journal: J. Amer. Math. Soc. 15 (2002), 419-442
MSC (1991): Primary 35L10, 35L70
Published electronically: December 19, 2001
MathSciNet review: 1887639
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Abstract: In an earlier work of the author it was proved that the Strichartz estimates for second order hyperbolic operators hold in full if the coefficients are of class $C^2$. Here we strengthen this and show that the same holds if the coefficients have two derivatives in $L^1(L^\infty)$. Then we use this result to improve the local theory for second order nonlinear hyperbolic equations.


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Additional Information

Daniel Tataru
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Address at time of publication: Department of Mathematics, University of California, Berkeley, California 94720
Email: tataru@math.northwestern.edu, tataru@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-01-00375-7
PII: S 0894-0347(01)00375-7
Keywords: Strichartz estimates, nonlinear wave equation
Received by editor(s): October 12, 1999
Received by editor(s) in revised form: April 12, 2001
Published electronically: December 19, 2001
Additional Notes: This research was partially supported by NSF grant DMS-9622942 and by an Alfred P. Sloan fellowship
Article copyright: © Copyright 2001 American Mathematical Society