We prove Strichartz estimates for the Schrodinger equation with an electromagnetic potential, in dimension n>2. The decay and regularity assumptions on the potentials are almost critical, i.e., close to the Coulomb case. In addition, we require repulsivity and a non trapping condition, which are expressed as smallness of suitable components of the potentials. However, the potentials themselves can be large, and we avoid completely any a priori spectral assumption on the operator. The proof is based on smoothing estimates and new Sobolev embeddings for spaces associated to magnetic potentials.

Endpoint Strichartz estimates for the magnetic Schroedinger equation

VISCIGLIA, NICOLA
2010-01-01

Abstract

We prove Strichartz estimates for the Schrodinger equation with an electromagnetic potential, in dimension n>2. The decay and regularity assumptions on the potentials are almost critical, i.e., close to the Coulomb case. In addition, we require repulsivity and a non trapping condition, which are expressed as smallness of suitable components of the potentials. However, the potentials themselves can be large, and we avoid completely any a priori spectral assumption on the operator. The proof is based on smoothing estimates and new Sobolev embeddings for spaces associated to magnetic potentials.
2010
D'Ancona, P; Fanelli, L; Vega, L; Visciglia, Nicola
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/136566
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 64
  • ???jsp.display-item.citation.isi??? 60
social impact