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Resonance-free region in scattering by a strictly convex obstacle

Arkiv för Matematik

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, Berkeley, CA, 94720, U.S.A.

    Long Jin

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  1. Long Jin
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Correspondence to Long Jin.

Additional information

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

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  • DOI: https://doi.org/10.1007/s11512-013-0185-0

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