Strichartz Estimates for the Schrödinger Equation with small Magnetic Potential
Journées équations aux dérivées partielles (2005), article no. 4, 17 p. 
@article{JEDP_2005____A4_0,
     author = {Georgiev, Vladimir and Stefanov, Atanas and Tarulli, Mirko},
     title = {Strichartz {Estimates} for the {Schr\"odinger} {Equation} with small {Magnetic} {Potential}},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {4},
     pages = {1--17},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2005},
     doi = {10.5802/jedp.17},
     mrnumber = {2352773},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jedp.17/}
}
TY  - JOUR
AU  - Georgiev, Vladimir
AU  - Stefanov, Atanas
AU  - Tarulli, Mirko
TI  - Strichartz Estimates for the Schrödinger Equation with small Magnetic Potential
JO  - Journées équations aux dérivées partielles
PY  - 2005
SP  - 1
EP  - 17
PB  - Groupement de recherche 2434 du CNRS
UR  - http://www.numdam.org/articles/10.5802/jedp.17/
DO  - 10.5802/jedp.17
LA  - en
ID  - JEDP_2005____A4_0
ER  - 
%0 Journal Article
%A Georgiev, Vladimir
%A Stefanov, Atanas
%A Tarulli, Mirko
%T Strichartz Estimates for the Schrödinger Equation with small Magnetic Potential
%J Journées équations aux dérivées partielles
%D 2005
%P 1-17
%I Groupement de recherche 2434 du CNRS
%U http://www.numdam.org/articles/10.5802/jedp.17/
%R 10.5802/jedp.17
%G en
%F JEDP_2005____A4_0
Georgiev, Vladimir; Stefanov, Atanas; Tarulli, Mirko. Strichartz Estimates for the Schrödinger Equation with small Magnetic Potential. Journées équations aux dérivées partielles (2005), article  no. 4, 17 p. doi : 10.5802/jedp.17. http://www.numdam.org/articles/10.5802/jedp.17/

[1] S. Agmon. Spectral properties of Schrödinger operators and scattering theory. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 2(2):151–218, 1975. | Numdam | MR | Zbl

[2] P. Alsholm and G. Schmidt. Spectral and scattering theory for Schrödinger operators. Arch. Rational Mech. Anal., 40:281–311, 1970/1971. | MR | Zbl

[3] A. A. Balinsky, W. D. Evans, R. T. Lewis, On the number of negative eigenvalues of Schrödinger operators with an Aharonov-Bohm magnetic field. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001), no. 2014, 2481–2489. | MR | Zbl

[4] J. A. Barcelo, A. Ruiz, and L. Vega. Weighted estimates for the Helmholtz equation and some applications. J. Funct. Anal. 150 (1997), 356–382. | MR | Zbl

[5] J. Bergh and J. Löfström, Interpolation spaces, Springer Berlin, Heidelberg, New York, 1976. | MR | Zbl

[6] V. Georgiev and M. Tarulli. Scale invariant energy smoothing estimates for the Scrödinger Equation with small Magnetic Potential. Preprint Universitá di Pisa, 2005.

[7] J. Ginibre and G. Velo. Generalized Strichartz inequalities for the wave equation. J. Funct. Anal., 133(1) (1995) 50–68. | MR | Zbl

[8] L. Hörmander, The analysis of linear partial differential operators. II. Differential operators with constant coefficients. Fundamental Principles of Mathematical Sciences, 257. Springer-Verlag, Berlin, 1983. | MR | Zbl

[9] A. Ionescu, C. Kenig, Well - posedness and local smoothing of solutions of Schrödinger equations preprint 2005.

[10] C. Kenig, G. Ponce, L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J., 40 (1991), 33–69. | MR | Zbl

[11] C. Kenig, G. Ponce, L. Vega, Small solutions to nonlinear Schrödinger equations., Ann. Inst. H. Poincaré Anal. Non Linéaire, 10 (1993), no. 3, 255–288. | Numdam | MR | Zbl

[12] C. Kenig, G. Ponce, L. Vega, Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations., Invent. Math., 134 (1998), no. 3, 489–545. | MR | Zbl

[13] M. Keel and T. Tao. Endpoint Strichartz estimates. Amer. J. Math., 120(5):955–980, 1998. | MR | Zbl

[14] I. Rodnianski, T. Tao, Global regularity for the Maxwell-Klein-Gordon equation with small critical Sobolev norm in high dientions. Comm. Math. Phys. 2005. | MR | Zbl

[15] A. Ruiz, L. Vega On local regularity of Schrödinger equations. Int. Math. Research Notes 1, 1993, 13 – 27 . | MR | Zbl

[16] A. Ruiz, L. Vega Local regularity of solutions to wave equations with time–dependent potentials. Duke Math. Journal 76, 1, 1994, 913 – 940. | MR | Zbl

[17] G. Staffilani, D. Tataru, Strichartz estimates for a Schrödinger operator with nonsmooth coefficients. Comm. Partial Differential Equations 27 (2002), no. 7-8, 1337–1372. | MR | Zbl

[18] E. Stein, Harmonic Analysis. Princeton Mathematical Series, Princeton Univ. Press, Princeton. | Zbl

[19] A. Stefanov Strichartz estimates for the magnetic Schrödinger equation preprint 2004. | Zbl

[20] M. Tarulli. Smoothing Estimates for Scalar Field with Electromagnetic Perturbation. EJDE. Vol. 2004(2004), No. 146, pp. 1-14. | Zbl

Cité par Sources :