Dispersion and strichartz inequalities for the one-dimensional schrödinger equation with variable coefficients

International Mathematics Research Notices

Volumn , Issue 11, 2005, Pages 687-700

  Salort, Delphine ^a  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17744373311     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/imrn.2005.687     Document Type: Article

References (19)

1. M. Avellaneda, G. Bardos, and J. Rauch, Contrôlabilité exacte, homogénéisation et localisation d'ondes dans un milieu non-homogène [Exact controllability, homogenization and localization of waves in a nonhomogeneous medium], Asymptotic Anal. 5 (1992), no. 6, 481-494 (French).
2. V. Banica, Dispersion and Strichartz inequalities for Schrödinger equations with singular coefficients, SIAM J. Math. Anal. 35 (2003), no. 4, 868-883.
3. N. Burq, P. Gérard, and N. Tzvetkov, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, Amer. J. Math. 126 (2004), no. 3, 569-605.
4. N. Burq and F. Planchon, Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications, preprint, 2004.
5. C. Castro and E. Zuazua, Concentration and lack of observability of waves in highly heterogeneous media, Arch. Ration. Mech. Anal. 164 (2002), no. 1, 39-72.
6. s, Nonlinear Anal. 14 (1990), no. 10, 807-836.
7. J.-Y. Chemin, Fluides parfaits incompressibles [Incompressible perfect fluids], Astérisque 230 (1995), 177 pp. (French).
8. W. Craig, T. Kappeler, and W. Strauss, Microlocal dispersive smoothing for the Schrödinger equation, Comm. Pure Appl. Math. 48 (1995), no. 8, 769-860.
9. S.-i. Doi, Remarks on the Cauchy problem for Schrödinger-type equations, Comm. Partial Differential Equations 21 (1996), no. 1-2, 163-178.
10. J. Ginibre and G. Velo, Smoothing properties and retarded estimates for some dispersive evolution equations, Comm. Math. Phys. 144 (1992), no. 1, 163-188.
11. A. Hassell, T. Tao, and J. Wunsch, Sharp Strichartz estimates on non-trapping asymptotically conic manifolds, submitted to Amer. J. Math.
12. N. Hayashi, K. Nakamitsu, and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension, Math. Z. 192 (1986), no. 4, 637-650.
13. L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis, 2nd ed., Springer Study Edition, Springer, Berlin, 1990.
14. M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), no. 5, 955-980.
15. S. Klainerman, A commuting vectorfields approach to Strichartz-type inequalities and applications to quasi-linear wave equations, Int. Math. Res. Not. 2001 (2001), no. 5, 221-274.
16. L. Robbiano and G. Zuily, Microlocal analytic smoothing effect for the Schrödinger equation, Duke Math. J. 100 (1999), no. 1, 93-129.
17. D. Salort, Inégalités de Strichartz et équation de type Schrödinger à coefficients variables, preprint, 2003.
18. _, Dispersion et inégalités de Strichartz pour l'équation de Schrödinger 1d à coefficients variables, submitted to C. R. Acad. Sci. Paris Sér. I Math.
19. G. Staffilani and D. Tataru, Strichartz estimates for a Schrödinger operator with nonsmooth coefficients, Comm. Partial Differential Equations 27 (2002), no. 7-8, 1337-1372.