Journal of the American Mathematical Society

Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III

Author(s): Daniel Tataru
Journal: J. Amer. Math. Soc. 15 (2002), 419-442.
MSC (1991): Primary 35L10, 35L70
Posted: December 19, 2001
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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

. 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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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: 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
Posted: December 19, 2001
Additional Notes: This research was partially supported by NSF grant DMS-9622942 and by an Alfred P. Sloan fellowship
Copyright of article: Copyright 2001, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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