Strichartz Estimates for the Wave Equation on Manifolds With Boundary

Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D.

doi:10.1016/j.anihpc.2008.12.004

Blair, Matthew D. ; Smith, Hart F. ; Sogge, Christopher D.

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1817-1829.

MR | 5 citations dans Numdam

DOI : 10.1016/j.anihpc.2008.12.004

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     author = {Blair, Matthew D. and Smith, Hart F. and Sogge, Christopher D.},
     title = {Strichartz {Estimates} for the {Wave} {Equation} on {Manifolds} {With} {Boundary}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1817--1829},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.12.004},
     mrnumber = {2566711},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.12.004/}
}

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Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. Strichartz Estimates for the Wave Equation on Manifolds With Boundary. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1817-1829. doi : 10.1016/j.anihpc.2008.12.004. http://www.numdam.org/articles/10.1016/j.anihpc.2008.12.004/

Bibliographie
Cité par

[1] Bahouri H., Gérard P., High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations, Amer. J. Math. 121 (1999) 131-175. | MR | Zbl

[2] Bahouri H., Shatah J., Decay Estimates for the Critical Wave Equation, Ann. Inst. H. Poincaré Anal. Non Lineáire 15 (6) (1998) 783-789. | Numdam | MR | Zbl

[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. | MR | Zbl

[4] Burq N., Global Strichartz Estimates for Nontrapping Geometries: About an Article by H. Smith and C. Sogge, Comm. Partial Differential Equations 28 (2003) 1675-1683. | MR | Zbl

[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. | MR

[6] N. Burq, F. Planchon, Global existence for energy critical waves in 3-d domains: Neumann boundary conditions, Amer. J. Math., in press. | MR

[7] Christ M., Kiselev A., Maximal Functions Asociated to Filtrations, J. Funct. Anal. 179 (2001) 409-425. | MR | Zbl

[8] Ginibre J., Velo G., Generalized Strichartz Inequalities for the Wave Equation, J. Funct. Anal. 133 (1995) 50-68. | MR | Zbl

[9] Grillakis M. G., Regularity for the Wave Equation With a Critical Nonlinearity, Comm. Pure Appl. Math. 45 (1992) 749-774. | MR | Zbl

[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. | MR

[11] Ivanovici O., Counter Examples to Strichartz Estimates for the Wave Equation in Domains, arXiv:0805.2901.

[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. | MR | Zbl

[13] Keel M., Tao T., Endpoint Strichartz Estimates, Amer. J. Math. 120 (1998) 955-980. | MR | Zbl

[14] Koch H., Tataru D., Dispersive Estimates for Principally Normal Operators, Comm. Pure Appl. Math. 58 (2005) 217-284. | MR | Zbl

[15] Lindblad H., Sogge C. D., On Existence and Scattering With Minimal Regularity for Semilinear Wave Equations, J. Funct. Anal. 130 (1995) 357-426. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[18] Morawetz C., Time Decay for the Nonlinear Klein-Gordon Equation, Proc. Roy. Soc. A. 306 (1968) 291-296. | MR | Zbl

[19] Shatah J., Struwe M., Regularity for the Wave Equation With a Critical Nonlinearity, Internat. Math. Res. Notices 7 (1994) 303-310. | MR | Zbl

[20] Smith H. F., A Parametrix Construction for Wave Equations With $C^{1, 1}$ Coefficients, Ann. Inst. Fourier (Grenoble) 48 (1998) 797-835. | Numdam | MR | Zbl

[21] Smith H. F., Spectral Cluster Estimates for $C^{1, 1}$ Estimates, Amer. J. Math. 128 (2006) 1069-1103. | MR

[22] Smith H. F., Sogge C. D., On the Critical Semilinear Wave Equation Outside Convex Obstacles, J. Amer. Math. Soc. 8 (1995) 879-916. | MR | Zbl

[23] Smith H. F., Sogge C. D., Global Strichartz Estimates for Nontrapping Perturbations of the Laplacian, Comm. Partial Differential Equations 25 (2000) 2171-2183. | MR | Zbl

[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. | MR

[25] Sogge C., Lectures on Nonlinear Wave Equations, International Press, Boston, MA, 1995. | MR | Zbl

[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. | MR | Zbl

[27] Tao T., Nonlinear Dispersive Equations: Local and Global Analysis, American Mathematical Society, Providence, RI, 2006. | MR | Zbl

[28] Tataru D., Strichartz Estimates for Second Order Hyperbolic Operators With Nonsmooth Coefficients III, J. Amer. Math. Soc. 15 (2002) 419-442. | MR | Zbl

[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. | MR | Zbl

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