Uniform Resolvent Estimates for Magnetic Schrödinger Operators in a 2D Exterior Domain and their Applications to Related Evolution Equations

Abstract

We consider the magnetic Schrödinger operator in an exterior domain $\Omega \subset {\mathbb{R}}^2$ with star-shaped boundary with respect to the origin. We prove uniform resolvent estimates under suitable decay and smallness conditions on the magnetic field and external potential. The results are then used to obtain smoothing properties for the corresponding evolution equations.