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| 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). |
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