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Arkiv för Matematik
Volume 55 (2017)
Number 1
Spectral analysis of the subelliptic oblique derivative problem
Pages: 243 – 270
DOI: https://dx.doi.org/10.4310/ARKIV.2017.v55.n1.a13
Author
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.
Keywords
oblique derivative problem, subelliptic operator, asymptotic eigenvalue distribution, Boutet de Monvel calculus
2010 Mathematics Subject Classification
35J25, 35P20, 35S05, 47D03
Received 16 March 2016
Accepted 29 September 2016
Published 26 September 2017