Some dispersive estimates for Schrödinger equations with repulsive potentials

Journal of Functional Analysis

Volumn 236, Issue 1, 2006, Pages 1-24

  Barceló, Juan A ^a   Ruiz, Alberto ^b   Vega, Luis ^c  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

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

Author keywords

Dispersive estimates; Energy methods; Schr dinger equations

Indexed keywords

EID: 33646121745     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.03.012     Document Type: Article

References (24)

1. Agmon S. Spectral properties of Schrödinger operators and scattering theory. Ann. Sc. Norm. Sup. Pisa Ser. 4 2 (1975) 121-218
2. Agmon S., and Hörmander L. Asymptotic properties of solutions of differential equations with simple characteristics. J. Anal. Math. 30 (1976)
3. Arai M. Absolute continuity of Hamiltonian operators with repulsive potentials. Publ. Res. Inst. Math. Sci. 7 (1971-1972) 621-635
4. J.A. Barceló, J. Bennett, A. Ruiz, Spherical perturbations of Schrödinger equations, J. Fourier Anal. Appl., in press
5. N. Burq, F. Planchon, J.G. Stalker, A.S. Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay, preprint
6. Constantin P., and Saut J.C. Local smoothing properties of dispersive equations. J. Amer. Math. Soc. 1 (1988) 413-419
7. Cycon H., Froese R.G., Kirsch W., and Simon B. Schrödinger Operators (1987), Springer-Verlag
8. Doi S. On the Cauchy problem for Schrödinger-type equations and the regularity of solution. J. Math. Kyoto Univ. 34 (1994) 319-328
9. Gasser I., Markowich P.A., and Perthame B. Dispersion and moments lemmas revisited. J. Differential Equations 156 (1999) 254-281
10. m ), m {greater than or slanted equal to} 5. Duke Math. J. 47 1 (1980) 57-80
11. 4 ). J. Math. Anal. Appl. 101 (1984) 397-422
12. Jensen A., and Kato T. Spectral properties of Schrödinger operators and time decay of the wave functions. Duke Math. J. 46 1 (1979) 583-611
13. Kerman R., and Sawyer E.T. The trace inequality and eigenvalue estimates for Schrödinger operators. Ann. Inst. Fourier (Grenoble) 36 (1986) 207-228
14. Lions P.L., and Perthame B. Lemmes de moments, de moyenne et de dispersion. C. R. Acad. Sci. Paris Sér. I Math. 314 (1992) 801-806
15. Murata M. Asymptotic expansions in time for solutions of Schrödinger-type equations. J. Funct. Anal. 49 (1982) 10-56
16. p-weighted inequalities. Ann. Inst. Fourier (Grenoble) 45 3 (1995) 809-824
17. Perthame B., and Vega L. Morrey-Campanato estimates for Helmholtz equations. J. Funct. Anal. 164 (1999) 340-355
18. Reed M., and Simon B. Methods of Modern Math. Physics. II Selfadjointness (1975), Academic Press
19. Reed M., and Simon B. Methods of Modern Math. Physics. IV Analysis of Operators (1978), Academic Press
20. Rodnianski I., and Schlag W. Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Invent. Math. 155 (2004) 455-513
21. Ruiz A., and Vega L. On local regularity of Schrödinger equations. Int. Math. Res. Not. 1 (1993) 13-17
22. Ruiz A., and Vega L. Local regularity of solutions to wave equations with time dependent potentials. Duke Math. J. 76 3 (1994) 913-940
23. Sjölin P. Regularity of solutions to the Schrödinger equations. Duke Math. J. 55 (1987) 699-715
24. Vega L. Schrödinger equations: Pointwise convergence to the initial data. Proc. Amer. Math. Soc. 102 (1988) 874-878