Arkiv för Matematik

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

Resonance-free region in scattering by a strictly convex obstacle

Long Jin

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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.

Note

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485802677

Digital Object Identifier
doi:10.1007/s11512-013-0185-0

Mathematical Reviews number (MathSciNet)
MR3255140

Zentralblatt MATH identifier
1317.35161

Rights
2013 © Institut Mittag-Leffler

Citation

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. https://projecteuclid.org/euclid.afm/1485802677


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