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Spectral analysis of the subelliptic oblique derivative problem

Kazuaki Taira University of Tsukuba

Analysis of PDEs mathscidoc:1803.43019

Arkiv for Matematik, 55, 2017
This paper is devoted to a functional analytic approach to the subelliptic oblique derivative problem for the usual Laplacian with a complex parameter λ. We solve the long-standing open problem of the asymptotic eigenvalue distribution for the homogeneous oblique derivative problem when |λ| tends to ∞. We prove the spectral properties of the closed realization of the Laplacian similar to the elliptic (non-degenerate) case. In the proof we make use of Boutet de Monvel calculus in order to study the resolvents and their adjoints in the framework of L2 Sobolev spaces.
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@inproceedings{kazuaki2017spectral,
  title={Spectral analysis of the subelliptic oblique derivative problem},
  author={Kazuaki Taira},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180301172035737595954},
  booktitle={Arkiv for Matematik},
  volume={55},
  year={2017},
}
Kazuaki Taira. Spectral analysis of the subelliptic oblique derivative problem. 2017. Vol. 55. In Arkiv for Matematik. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180301172035737595954.
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