Abstract
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.
Citation
Long Jin. "Resonance-free region in scattering by a strictly convex obstacle." Ark. Mat. 52 (2) 257 - 289, October 2014. https://doi.org/10.1007/s11512-013-0185-0
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