Strichartz estimates for the wave equation on manifolds with boundary

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire - Tập 26 Số 5 - Trang 1817-1829 - 2009
Matthew D. Blair1, Hart F. Smith2, Christopher D. Sogge3
1Department of Mathematics, University of New Mexico, Albuquerque, NM 87131, USA
2Department of Mathematics, University of Washington, Seattle, WA 98195, USA
3Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA

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Tài liệu tham khảo

Bahouri, 1999, High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math., 121, 131, 10.1353/ajm.1999.0001

Bahouri, 1998, Decay estimates for the critical wave equation, Ann. Inst. H. Poincaré Anal. Non Lineáire, 15, 783, 10.1016/S0294-1449(99)80005-5

Bchatnia, 2004, Scattering and exponential decay of the local energy for the solutions of semilinear and subcritical wave equation outside convex obstacle, Math. Z., 247, 619, 10.1007/s00209-003-0638-4

Burq, 2003, Global Strichartz estimates for nontrapping geometries: about an article by H. Smith and C. Sogge, Comm. Partial Differential Equations, 28, 1675, 10.1081/PDE-120024528

Burq, 2008, Global existence for energy critical waves in 3-D domains, J. Amer. Math. Soc., 21, 831, 10.1090/S0894-0347-08-00596-1

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

Christ, 2001, Maximal functions asociated to filtrations, J. Funct. Anal., 179, 409, 10.1006/jfan.2000.3687

Ginibre, 1995, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., 133, 50, 10.1006/jfan.1995.1119

Grillakis, 1992, Regularity for the wave equation with a critical nonlinearity, Comm. Pure Appl. Math., 45, 749, 10.1002/cpa.3160450604

Hidano

Ivanovici

Kapitanski, 1991, Norm estimates in Besov and Lizorkin–Treibel spaces for the solutions of second order linear hyperbolic equations, J. Soviet Math., 56, 2348, 10.1007/BF01671936

Keel, 1998, Endpoint Strichartz estimates, Amer. J. Math., 120, 955, 10.1353/ajm.1998.0039

Koch, 2005, Dispersive estimates for principally normal operators, Comm. Pure Appl. Math., 58, 217, 10.1002/cpa.20067

Lindblad, 1995, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal., 130, 357, 10.1006/jfan.1995.1075

Metcalfe, 2004, Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle, Trans. Amer. Math. Soc., 356, 4839, 10.1090/S0002-9947-04-03667-0

Mockenhaupt, 1993, Local smoothing of Fourier integral operators and Carleson–Sjölin estimates, J. Amer. Math. Soc., 6, 65

Morawetz, 1968, Time decay for the nonlinear Klein–Gordon equation, Proc. Roy. Soc. A., 306, 291

Shatah, 1994, Regularity for the wave equation with a critical nonlinearity, Internat. Math. Res. Notices, 7, 303, 10.1155/S1073792894000346

Smith, 1998, A parametrix construction for wave equations with C1,1 coefficients, Ann. Inst. Fourier (Grenoble), 48, 797, 10.5802/aif.1640

Smith, 2006, Spectral cluster estimates for C1,1 estimates, Amer. J. Math., 128, 1069, 10.1353/ajm.2006.0041

Smith, 1995, On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc., 8, 879, 10.1090/S0894-0347-1995-1308407-1

Smith, 2000, Global Strichartz estimates for nontrapping perturbations of the Laplacian, Comm. Partial Differential Equations, 25, 2171, 10.1080/03605300008821581

Smith, 2007, On the Lp norm of spectral clusters for compact manifolds with boundary, Acta Math., 198, 107, 10.1007/s11511-007-0014-z

Sogge, 1995

Strichartz, 1977, Restriction of Fourier transform to quadratic surfaces and decay of solutions to the wave equation, Duke Math. J., 44, 705, 10.1215/S0012-7094-77-04430-1

Tao, 2006

Tataru, 2002, Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III, J. Amer. Math. Soc., 15, 419, 10.1090/S0894-0347-01-00375-7

Tataru, 2004, Phase space transforms and microlocal analysis, 505