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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.3 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000300014 

CUBO A Mathematical Journal Vol.12, N°03, (213–239). October 2010

 

Strichartz Estimates for the Schrödinger Equation

 

ELENA CORDERO AND DAVIDE ZUCCO

Department of Mathematics, University of Torino, v. Carlo Alberto 10, Torino, Italy email: elena.cordero@unito.it, email: davide.zucco@unito.it


ABSTRACT

The objective of this paper is to report on recent progress on Strichartz estimates for the Schrödinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in Wiener amalgam and modulation spaces. We present and compare the different technicalities. Then, we illustrate applications to well-posedness.

Keywords and phrases: Dispersive estimates, Strichartz estimates, Wiener amalgam spaces, Modulation spaces, Schrödinger equation.


RESUMEN

El objetivo de este trabajo es reportar los progresos recientes sobre estimativas de Strichartz para la ecuación de Schrödinger y presentar el estado de arte. Estas estimativas han sido obtenidas en espacios de Lebesgue, espacios de Sobolev, y recientemente, en espacios de Wiener amalgamados y de modulación. Presentamos y comparamos los diferentes aspectos técnicos envueltos. Ilustramos los resultados con aplicaciones a buena colocación.

Math. Subj. Class.: 42B35,35B65, 35J10, 35B40.


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