Arkiv för Matematik

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  • Volume 52, Number 2 (2014), 257-289.

Resonance-free region in scattering by a strictly convex obstacle

Long Jin

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We prove the existence of a resonance-free region in scattering by a strictly convex obstacle $\mathcal{O}$ with the Robin boundary condition $\partial_{\nu}u+\gamma u|_{\partial\mathcal{O}}=0$. More precisely, we show that the scattering resonances lie below a cubic curve ℑζ=−S|ζ|1/3+C. The constant S is the same as in the case of the Neumann boundary condition γ=0. This generalizes earlier results on cubic pole-free regions obtained for the Dirichlet boundary condition.


The author would like to thank Maciej Zworski for the encouragement and advices during the preparation of this paper. Partial support by the National Science Foundation grant DMS-1201417 is also gratefully acknowledged.

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Ark. Mat., Volume 52, Number 2 (2014), 257-289.

Received: 11 December 2012
First available in Project Euclid: 30 January 2017

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2013 © Institut Mittag-Leffler


Jin, Long. Resonance-free region in scattering by a strictly convex obstacle. Ark. Mat. 52 (2014), no. 2, 257--289. doi:10.1007/s11512-013-0185-0.

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