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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afm/1517535612

Digital Object Identifier
doi:10.4310/ARKIV.2017.v55.n1.a13

Mathematical Reviews number (MathSciNet)
MR3711152

Zentralblatt MATH identifier
06823283

Subjects
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}

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

Citation

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. https://projecteuclid.org/euclid.afm/1517535612


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