Counterexamples of Strichartz inequalities for Schrödinger equations with repulsive potentials

International Mathematics Research Notices

Volumn 2006, Issue , 2006, Pages 1-16

  Goldberg, Michael ^a   Vega, Luis ^b   Visciglia, Nicola ^c  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^c UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645677003     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/IMRN/2006/13927     Document Type: Article

References (23)

1. J. A. Barcelo A. Ruiz L. Vega Some dispersive estimates for Schrödinger equations with repulsive potentials. preprint, 2004
2. N. Burq F. Planchon J. G. Stalker A. S. Tahvildar-Zadeh Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential. Journal of Functional Analysis 203 2003 2 519 549
3. N. Burq F. Planchon J. G. Stalker A. S. Tahvildar-Zadeh Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay. Indiana University Mathematics Journal 53 2004 6 1665 1680
4. M. Christ A. Kiselev Maximal functions associated to filtrations. Journal of Functional Analysis 179 2001 2 409 425
5. P. Constantin J.-C. Saut Local smoothing properties of dispersive equations. Journal of the American Mathematical Society 1 1988 2 413 439
6. P. Constantin J.-C. Saut Local smoothing properties of Schrödinger equations. Indiana University Mathematics Journal 38 1989 3 791 810
7. P. D'Ancona V. Pierfelice N. Visciglia Some remarks on the Schrödinger equation with potential in Ltr Lxs. Mathematische Annalen 333 2005 2 271-290
8. M. Goldberg Dispersive bounds for the three-dimensional Schrödinger equation with almost critical potentials. to appear in Geometric and Functional Analysis
9. I. W. Herbst Spectral and scattering theory for Schrödinger operators with potentials independent of x American Journal of Mathematics 113 1991 3 509 565
10. I. W. Herbst E. Skibsted Quantum scattering for potentials independent of x: asymptotic completeness for high and low energies. Communications in Partial Differential Equations 29 2004 3-4 547 610
11. J.-L. Journé A. Soffer C. D. Sogge Decay estimates for Schrödinger operators. Communications on Pure and Applied Mathematics 44 1991 5 573 604
12. M. Keel T. Tao Endpoint Strichartz estimates. American Journal of Mathematics 120 1998 5 955 980
13. C. E. Kenig G. Ponce L. Vega Small solutions to nonlinear Schrödinger equations. Annales de l'Institut Henri Poincaré. Analyse Non Linéaire 10 1993 3 255 288
14. B. Perthame L. Vega Energy concentration and Sommerfeld condition for Helmholtz and Liouville equations. Comptes Rendus Mathématique. Académie des Sciences. Paris 337 2003 9 587 592
15. B. Perthame L. Vega Energy decay and Sommerfield condition for Helmholtz equation with variable index at infinity. preprint, 2005
16. I. Rodnianski W. Schlag Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Inventiones Mathematicae 155 2004 3 451 513
17. A. Ruiz L. Vega On local regularity of Schrödinger equations. International Mathematics Research Notices 1993 1993 1 13 27
18. A. Ruiz L. Vega Local regularity of solutions to wave equations with time-dependent potentials. Duke Mathematical Journal 76 1994 3 913 940
19. W. Schlag Dispersive estimates for Schrödinger operators: a survey. preprint, 2005
20. P. Sjölin Regularity of solutions to the Schrödinger equation. Duke Mathematical Journal 55 1987 3 699 715
21. G. Staffilani D. Tataru Strichartz estimates for a Schrödinger operator with nonsmooth coefficients. Communications in Partial Differential Equations 27 2002 7-8 1337 1372
22. L. Vega Schrödinger equations: pointwise convergence to the initial data. Proceedings of the American Mathematical Society 102 1988 4 874 878
23. L. Vega N. Visciglia On the local smoothing for the Schrödinger equation. preprint, 2005