Resonance-free region in scattering by a strictly convex obstacle

Long Jin Department of Mathematics, University of California, Berkeley

Analysis of PDEs Functional Analysis mathscidoc:1701.03029

Arkiv for Matematik, 52, (2), 257-289, 2012.12
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 ℑ$ζ$=−$S$|$ζ$|^{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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@inproceedings{long2012resonance-free,
  title={Resonance-free region in scattering by a strictly convex obstacle},
  author={Long Jin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637994531064},
  booktitle={Arkiv for Matematik},
  volume={52},
  number={2},
  pages={257-289},
  year={2012},
}
Long Jin. Resonance-free region in scattering by a strictly convex obstacle. 2012. Vol. 52. In Arkiv for Matematik. pp.257-289. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637994531064.
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