Strichartz estimates for the wave equation on manifolds with boundary

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1. [1] Bahouri H., Gérard P., High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math.121 (1999) 131-175. Zbl0919.35089MR1705001
2. [2] Bahouri H., Shatah J., Decay estimates for the critical wave equation, Ann. Inst. H. Poincaré Anal. Non Lineáire15 (6) (1998) 783-789. Zbl0924.35084MR1650958
3. [3] Bchatnia A., Daoulatli M., Scattering and exponential decay of the local energy for the solutions of semilinear and subcritical wave equation outside convex obstacle, Math. Z.247 (2004) 619-642. Zbl1063.35033MR2114432
4. [4] Burq N., Global Strichartz estimates for nontrapping geometries: about an article by H. Smith and C. Sogge, Comm. Partial Differential Equations28 (2003) 1675-1683. Zbl1026.35020MR2001179
5. [5] Burq N., Lebeau G., Planchon F., Global existence for energy critical waves in 3-D domains, J. Amer. Math. Soc.21 (2008) 831-845. Zbl1184.35210MR2393429
6. [6] N. Burq, F. Planchon, Global existence for energy critical waves in 3-d domains: Neumann boundary conditions, Amer. J. Math., in press. Zbl1184.35210MR2567505
7. [7] Christ M., Kiselev A., Maximal functions asociated to filtrations, J. Funct. Anal.179 (2001) 409-425. Zbl0974.47025MR1809116
8. [8] Ginibre J., Velo G., Generalized Strichartz inequalities for the wave equation, J. Funct. Anal.133 (1995) 50-68. Zbl0849.35064MR1351643
9. [9] Grillakis M.G., Regularity for the wave equation with a critical nonlinearity, Comm. Pure Appl. Math.45 (1992) 749-774. Zbl0785.35065MR1162370
10. [10] Hidano K., Metcalfe J., Smith H.F., Sogge C.D., Zhou Y., On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles, arXiv:0805.1673. Zbl1193.35100MR2584618
11. [11] Ivanovici O., Counter examples to Strichartz estimates for the wave equation in domains, arXiv:0805.2901. Zbl1201.35060
12. [12] Kapitanski L.V., Norm estimates in Besov and Lizorkin–Treibel spaces for the solutions of second order linear hyperbolic equations, J. Soviet Math.56 (1991) 2348-2389. Zbl0759.35014MR1031987
13. [13] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math.120 (1998) 955-980. Zbl0922.35028MR1646048
14. [14] Koch H., Tataru D., Dispersive estimates for principally normal operators, Comm. Pure Appl. Math.58 (2005) 217-284. Zbl1078.35143MR2094851
15. [15] Lindblad H., Sogge C.D., On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal.130 (1995) 357-426. Zbl0846.35085MR1335386
16. [16] Metcalfe J., Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle, Trans. Amer. Math. Soc.356 (2004) 4839-4855. Zbl1060.35026MR2084401
17. [17] Mockenhaupt G., Seeger A., Sogge C.D., Local smoothing of Fourier integral operators and Carleson–Sjölin estimates, J. Amer. Math. Soc.6 (1993) 65-130. Zbl0776.58037MR1168960
18. [18] Morawetz C., Time decay for the nonlinear Klein–Gordon equation, Proc. Roy. Soc. A.306 (1968) 291-296. Zbl0157.41502MR234136
19. [19] Shatah J., Struwe M., Regularity for the wave equation with a critical nonlinearity, Internat. Math. Res. Notices7 (1994) 303-310. Zbl0830.35086MR1283026
20. [20] Smith H.F., A parametrix construction for wave equations with $C^{1,1}$ coefficients, Ann. Inst. Fourier (Grenoble)48 (1998) 797-835. Zbl0974.35068MR1644105
21. [21] Smith H.F., Spectral cluster estimates for $C^{1,1}$ estimates, Amer. J. Math.128 (2006) 1069-1103. Zbl1284.35149MR2262171
22. [22] Smith H.F., Sogge C.D., On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc.8 (1995) 879-916. Zbl0860.35081MR1308407
23. [23] Smith H.F., Sogge C.D., Global Strichartz estimates for nontrapping perturbations of the Laplacian, Comm. Partial Differential Equations25 (2000) 2171-2183. Zbl0972.35014MR1789924
24. [24] Smith H.F., Sogge C.D., On the $L^p$ norm of spectral clusters for compact manifolds with boundary, Acta Math.198 (2007) 107-153. Zbl1189.58017MR2316270
25. [25] Sogge C., Lectures on Nonlinear Wave Equations, International Press, Boston, MA, 1995. Zbl1089.35500MR1715192
26. [26] Strichartz R., Restriction of Fourier transform to quadratic surfaces and decay of solutions to the wave equation, Duke Math. J.44 (1977) 705-714. Zbl0372.35001MR512086
27. [27] Tao T., Nonlinear Dispersive Equations: Local and Global Analysis, American Mathematical Society, Providence, RI, 2006. Zbl1106.35001MR2233925
28. [28] Tataru D., Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III, J. Amer. Math. Soc.15 (2002) 419-442. Zbl0990.35027MR1887639
29. [29] Tataru D., Phase space transforms and microlocal analysis, in: Phase Space Analysis of Partial Differential Equations, vol. II, Pubbl. Cent. Ric. Mat. Ennio Georgi, Scuola Norm. Sup., Pisa, 2004, pp. 505-524. Zbl1111.35143MR2208883

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