Regularizing estimates for Schrödinger and wave equations
Journées équations aux dérivées partielles (1993), article no. 5, 12 p.
Alberto Ruiz. Regularizing estimates for Schrödinger and wave equations. Journées équations aux dérivées partielles (1993), article  no. 5, 12 p.. doi: 10.5802/jedp.444
@incollection{JEDP_1993____A5_0,
     author = {Alberto Ruiz},
     title = {Regularizing estimates for {Schr\"odinger} and wave equations},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {5},
     pages = {1--12},
     year = {1993},
     publisher = {\'Ecole polytechnique},
     doi = {10.5802/jedp.444},
     zbl = {0797.35020},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.444/}
}
TY  - JOUR
AU  - Alberto Ruiz
TI  - Regularizing estimates for Schrödinger and wave equations
JO  - Journées équations aux dérivées partielles
PY  - 1993
SP  - 1
EP  - 12
PB  - École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.444/
DO  - 10.5802/jedp.444
LA  - en
ID  - JEDP_1993____A5_0
ER  - 
%0 Journal Article
%A Alberto Ruiz
%T Regularizing estimates for Schrödinger and wave equations
%J Journées équations aux dérivées partielles
%] 5
%D 1993
%P 1-12
%I École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.444/
%R 10.5802/jedp.444
%G en
%F JEDP_1993____A5_0

[AH] Agmon S., Hörmander L., Asymptotic properties of solutions of differential equations with simple characteristics. J. d'Analyse Mathématique, Vol. 30, 1976, 1-28 | MR | Zbl

[ChR] Chiarenza F., Ruiz A., Uniform L2 weighted Sobolev inequalities. Proc. AMS., 112, (1), 1991, 53-64. | MR | Zbl

[ChF] Chiarenza, Frasca, A remark on a paper by C. Fefferman. Proc AMS, 1990 | Zbl

[CS1] Constantin P., Saut J.C., Local smoothing properties of dispersive equations. J. of the AMS, 1, 1988, 413-139. | MR | Zbl

[CS2] Constantin P., Saut J.C., Local smoothing properties of Schrödinger equations. Indiana U. Math. J., 38, 3, 1989, 791-810. | MR | Zbl

[FP] C. Fefferman, P.Phong, Lower bounds for Schrödinger equations. Journes Eqs. D. P. St. Jean de Monts 1982. | Numdam | Zbl

[H] Harmse, J. On Lebesgue space estimates for the wave equation. Indiana University Math Journal 39.1 1990 | MR | Zbl

[LP] Lions P.L., Perthame B., Lemmes de moments, de moyenne et de dispersion. C.R. Acad. Sci. Paris, t 314, Série, p. 801-806. 1992. | MR | Zbl

[K] Kato T. On the Cauchy problem for the (generalized) KdV equation. Adv. in Math. Supplementary Studies, Studies in Applied Math., 8, 1983, 93-128. | MR | Zbl

[KY] Kato T., Yajima K., Some examples of smooth operators and the associated smoothing effect. Review in Math. Physics, 1, 4, 1989. | MR | Zbl

[KPV2] Kenig C., Ponce G., Vega L., Small solutions for non linear Schrödinger equations. To appear in Ann. I. Henri Poincaré. | Numdam | Zbl

[KRS] Kenig C., Ruiz A., Sogge C., Uniform Sobolev inequalities and unique continuation for second order constant coefficients differential operators. Duke Math. J., 55, 1987, 329-347. | MR | Zbl

[RV] Ruiz A., Vega L., Unique continuation for Schrödinger operators with potential in Morrey spaces. Publications Matemátiques, 35, 1991, 291-298. | MR | Zbl

[RV2] Ruiz A., Vega L., On local regularity of Schrödinger equations. Int. Math. Research Notices. N 1. 13-27. Duke Math. J. 1993 | MR | Zbl

[RV3] Smoothing effect for Schródinger and wave equations. In preparation

[SSj] Sjögren P., Sjölin P., Convergence properties for the time dependent Schrödinger equation. To appear in Ann. Acad. Sci. Fenn.. | Zbl

[Sj] Sjölin P., Regularity of solutions to the Schrödinger equations. Duke Math. J., 55, 1987, 699-715. | Zbl

[So] Soffer A., Phase space analysis of non linear waves and global existence. Preprint.

[T] Tomas P., A restriction theorem for the Fourier transform. Bull. AMS, 81, 1975, 477-478. | MR | Zbl

[V1] Vega L., Schrödinger equations : pointwise convergence to the initial data. Proc. AMS, 102, 1988, 874-878. | MR | Zbl

[V2] Vega L., El multiplicador de Schrödinger : la función maximal y los operadores de restricción. Tesis doctoral. Universidad Autónoma de Madrid. 1988.

[Y] Yajima K., Existence of solutions for Schrödinger Evolution Equations. Comm. Math. Phys., 110 (1987), 415-426. | MR | Zbl

Cité par Sources :