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 Title Sharp uniform resolvent estimate for Helmholtz and Schr\"odinger equations in an exterior domain in ${\mathbb R}^2$ and their applications.
 Name Hideo Nakazawa Country Japan Email nakazawa-hideo@nms.ac.jp Co-Author(s) Kiyoshi Mochizuki Submit Time 2014-02-27 02:11:36 Session Special Session 60: Recent advances in evolutionary equations
 Contents Sharp uniform resolvent estimate for Helmholtz and Schr\"odinger equations in an exterior domain in ${\mathbb R}^2$ is presented. Our inequality is obtained by noting the weight function which appears in Hardy inequality in an exterior domain in ${\mathbb R}^2$, and the duality in the both sides of our inequality is kept. As applications, some smoothing estimates for time dependent Schr\"odinger or wave equations are obtained. This is a joint work with Prof. Kiyoshi Mochizuki (Emeritus, Tokyo Metropolitan University).