Strichartz estimates for Schrödinger equations with variable coefficients  [ Inégalités de Strichartz pour l’équation de Schrödinger à coefficients variables ] (2005)


Robbiano, Luc; Zuily, Claude
Mémoires de la Société Mathématique de France, Tome 101-102 (2005) vi-208 p doi : 10.24033/msmf.414
URL stable : http://www.numdam.org/item?id=MSMF_2005_2_101-102__1_0

Bibliographie

[1] N. Burq« Estimations de Strichartz pour des perturbations à longue portée de l’opérateur de Schrödinger », in Séminaire Equations aux Dérivées Partielles, 2001-2002, École polytechnique, exp.no 11.

[2] N. Burq, P. Gérard & N. Tzvetkov« Strichartz inequalities and the non linear Schrödinger equation on compact manifold », Amer. J. Math. 126 (2004), p. 569–605. Zbl 1067.58027 | MR 2058384

[3] M. Christ & A. Kiselev« Maximal functions associatef to filtrations », J. Funct. Anal. 179 (2001), no. 2, p. 409–425. Zbl 0974.47025 | MR 1809116

[4] G.M. Constantin & T.H. Savits« A multivariate Faa di Bruno formula with applications », Trans. Amer. Math. Soc. 348 (1996), no. 2, p. 503–520. Zbl 0846.05003

[5] S.I. Doi« Smoothing effects of Schrödinger evolution groups on Riemannian manifolds », Duke Math. J. 82 (1996), p. 679–706. Zbl 0870.58101 | MR 1387689

[6] J. Ginibre & G. Velo« Smoothing properties and retarded estimates for some dispersive evolutions », Comm. Math. Phys. 144 (1992), p. 163–188. Zbl 0762.35008 | MR 1151250

[7] A. Hassell, T. Tao & J. Wunsch« A Strichartz inequality for the Schrödinger equation on non trapping asymptotically conic manifold », preprint. MR 2131050

[8] —, « Sharp Strichartz estimates on non trapping asymptotically conic manifolds », preprint.

[9] L. HörmanderThe analysis of linear partial differential operators, vol. I & IV, Grundhehren, Springer. Zbl 0388.47032 | MR 717035

[10] M. Kell & T. Tao« End point Strichartz estimate », Amer. J. Math. 120 (1998), p. 955–980. MR 1646048

[11] A. Melin & J. Sjöstrand« Fourier integral operators with complex valued phase function », Lect. Notes in Math., vol. 459, Springer, p. 121–223. MR 431289

[12] L. Robbiano & C. ZuilyAnalytic theory for the quadratic scattering wave front set and application to the Schrödinger equation, Astérisque, vol. 283, Société Mathématique de France, 2002. Zbl 1029.35001 | MR 1958605

[13] J. SjöstrandSingularités analytiques microlocales, Astérisque, vol. 95, Société Mathématique de France, 1982. Zbl 0524.35007 | MR 699623

[14] H. Smith & C. Sogge« Global Strichartz estimates for non trapping perturbations of the Laplacian », Comm. Partial Differential Equations 25 (2000), no. 11 & 12, p. 2171–2183. Zbl 0972.35014 | MR 1789924

[15] G. Staffilani & D. Tataru« Strichartz estimates for a Schrödinger operator with non smooth coefficients », Comm. Partial Differential Equations (2002), no. 5 & 6, p. 1337–1372. Zbl 1010.35015 | MR 1924470

[16] R. Strichartz« Restriction of Fourier transform to quadratic surfaces and decay of solutions to the wave equation », Duke Math. J. 44 (1977), p. 705–714. Zbl 0372.35001 | MR 512086

[17] K. Yajima« Existence of solutions for Schrödinger evolution equations », Comm. Math. Phys. 110 (1987), p. 415–426. Zbl 0638.35036 | MR 891945