Uniform Resolvent Estimates for Magnetic Schrödinger Operators in a 2D Exterior Domain and their Applications to Related Evolution Equations
Kiyoshi Mochizuki
Chuo University, Tokyo, JapanHideo Nakazawa
Nippon Medical School, Tokyo, Japan
![Uniform Resolvent Estimates for Magnetic Schrödinger Operators in a 2D Exterior Domain and their Applications to Related Evolution Equations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-prims-volume-51-issue-2.png&w=3840&q=90)
Abstract
We consider the magnetic Schrödinger operator in an exterior domain 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.
Cite this article
Kiyoshi Mochizuki, Hideo Nakazawa, Uniform Resolvent Estimates for Magnetic Schrödinger Operators in a 2D Exterior Domain and their Applications to Related Evolution Equations. Publ. Res. Inst. Math. Sci. 51 (2015), no. 2, pp. 319–336
DOI 10.4171/PRIMS/157