Strichartz estimates for wave equations with coefficients of sobolev regularity

Communications in Partial Differential Equations

Volumn 31, Issue 5, 2006, Pages 649-688

  Blair, Matthew ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Dispersive estimates; Strichartz estimates; Wave equation; Wave packets

Indexed keywords

EID: 33646370539     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300600635053     Document Type: Article

References (17)

1. Bahouri, H., Chemin, J.-Y. (1999a). Equations d'ondes quasilineares et effet dispersif, Int. Math. Res. Not. 21:1141-1178.
2. Bahouri, H., Chemin, J.-Y. (1999b). Equations d'ondes quasilineares et estimations de Strichartz. Amer. J. Math. 121(6):1337-1377.
3. Ginibre, J., Velo, G. (1995). Generalized Strichartz inequalities for the wave equation. J. Funct. Anal. 133(1):50-68.
4. Kapitanski, L. V. (1991). Norm estimates in Besov and Lizorkin-Treibel spaces for the solutions of second order linear hyperbolic equations. J. Sov. Math. 56(2):2348-2389.
5. Keel, M., Tao, T. (1998). Endpoint Strichartz estimates. Amer. J. Math. 120:955-980.
6. Lindblad, H., Sogge, C. D. (1995). On existence and scattering with minimal regularity for semilinear wave equations. J. Funct. Anal. 130(2):357-426.
7. Mockenhaupt, G., Seeger, A., Sogge, C. D. (1993). Local smoothing of Fourier integral operators and Carleson-Sjölin estimates. J. Amer. Math. Soc. 6(1):65-130.
8. 1,1 coefficients. Ann. Inst. Fourier (Grenoble) 48(3):797-835.
9. Smith, H., Sogge, C. (1994). On Strichartz and eigenfunction estimates for low regularity metrics. Math. Res. Lett. 1(6):729-737.
10. Stein, E. M. (1970). Singular Integrals and Differentiability Properties of Functions. Princeton, N.J.: Princeton University Press.
11. Stein, E. M. (1993). Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton, N.J.: Princeton University Press.
12. Strichartz, R. (1970). A priori estimates for the wave equation and some applications. J. Funct. Analysis 5:218-235.
13. Strichartz, R. (1977). Restriction of Fourier transform to quadratic surfaces and decay of solutions to the wave equation. Duke Math. J. 44(3):705-714.
14. Tataru, D. (2000). Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients and the nonlinear wave equation. Amer. J. Math. 122(2):349-376.
15. Tataru, D. (2001). Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients II. Amer. J. Math. 123(3):385-423.
16. Tataru, D. (2002). Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III. J. Amer. Math. Soc. 15(2):419-442.
17. Taylor, M. E. (1991). Pseudodifferential Operators and Nonlinear PDE. Boston: Birkhhäuser.