Non-trapping magnetic fields and Morrey-Campanato estimates for Schroedinger operators

Abstract

We prove some uniform in $\epsilon$ a priori estimates for solutions of the equation $$(\nabla -iA{)}^{2}u-V(x)u+(\lambda \pm i\epsilon )u=f,\lambda \ge 0,\epsilon \ne 0.$$ The estimates are obtained in terms of Morrey-Campanato norms, and can be used to prove absence of zero-resonances, in a suitable sense, for electromagnetic Hamiltonians. Precise conditions on the size of the \textit{trapping component} of the magnetic field and the non repulsive component of the electric field are given.

18 pages