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

Mochizuki Kiyoshi<sup>*</sup>; Nakazawa Hideo

doi:10.4171/PRIMS/157

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

作者：Mochizuki Kiyoshi^*; Nakazawa Hideo

来源：Publications of the Research Institute for Mathematical Sciences, 2015, 51(2): 319-336.

DOI：10.4171/PRIMS/157

摘要

We consider the magnetic Schrodinger operator in an exterior domain Omega subset of 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.