Arkiv för Matematik

  • Ark. Mat.
  • Volume 55, Number 1 (2017), 243-270.

Spectral analysis of the subelliptic oblique derivative problem

Kazuaki Taira

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This paper is devoted to a functional analytic approach to the subelliptic oblique derivative problem for the usual Laplacian with a complex parameter $\lambda$. We solve the long-standing open problem of the asymptotic eigenvalue distribution for the homogeneous oblique derivative problem when $\lvert \lambda \rvert$ tends to $\infty$. 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 $L^2$ Sobolev spaces.

Article information

Ark. Mat., Volume 55, Number 1 (2017), 243-270.

Received: 16 March 2016
First available in Project Euclid: 2 February 2018

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Zentralblatt MATH identifier

Primary: 35J25: Boundary value problems for second-order elliptic equations 35P20: Asymptotic distribution of eigenvalues and eigenfunctions 35S05: Pseudodifferential operators 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}

oblique derivative problem subelliptic operator asymptotic eigenvalue distribution Boutet de Monvel calculus


Taira, Kazuaki. Spectral analysis of the subelliptic oblique derivative problem. Ark. Mat. 55 (2017), no. 1, 243--270. doi:10.4310/ARKIV.2017.v55.n1.a13.

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