We prove Strichartz estimates for the Schrodinger equation with an electromagnetic potential, in dimension n >= 3. 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 nontrapping condition, which are expressed as smallness of suitable components of the potentials, while the potentials themselves can be large. The proof is based on smoothing estimates and new Sobolev embeddings for spaces associated to magnetic potentials. (C) 2010 Elsevier Inc. All rights reserved.
Endpoint Strichartz estimates for the magnetic Schrödinger equation / D'Ancona, Piero Antonio; Fanelli, Luca; Luis, Vega; Nicola, Visciglia. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 258:10(2010), pp. 3227-3240. [10.1016/j.jfa.2010.02.007]
Endpoint Strichartz estimates for the magnetic Schrödinger equation
D'ANCONA, Piero Antonio;FANELLI, Luca;
2010
Abstract
We prove Strichartz estimates for the Schrodinger equation with an electromagnetic potential, in dimension n >= 3. 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 nontrapping condition, which are expressed as smallness of suitable components of the potentials, while the potentials themselves can be large. The proof is based on smoothing estimates and new Sobolev embeddings for spaces associated to magnetic potentials. (C) 2010 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
