Open Access
October 2014 Resonance-free region in scattering by a strictly convex obstacle
Long Jin
Author Affiliations +
Ark. Mat. 52(2): 257-289 (October 2014). DOI: 10.1007/s11512-013-0185-0


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.

Funding Statement

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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Long Jin. "Resonance-free region in scattering by a strictly convex obstacle." Ark. Mat. 52 (2) 257 - 289, October 2014.


Received: 11 December 2012; Published: October 2014
First available in Project Euclid: 30 January 2017

zbMATH: 1317.35161
MathSciNet: MR3255140
Digital Object Identifier: 10.1007/s11512-013-0185-0

Rights: 2013 © Institut Mittag-Leffler

Vol.52 • No. 2 • October 2014
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