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

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.
D'Ancona, P; Fanelli, L; Vega, L; Visciglia, Nicola
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/136566
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