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.
|Autori:||D'ANCONA P; FANELLI L; VEGA L; VISCIGLIA N|
|Titolo:||Endpoint Strichartz estimates for the magnetic Schroedinger equation|
|Anno del prodotto:||2010|
|Digital Object Identifier (DOI):||10.1016/j.jfa.2010.02.007,|
|Appare nelle tipologie:||1.1 Articolo in rivista|