Spectral analysis of the subelliptic oblique derivative problem

摘要

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 vertical bar lambda vertical bar tends to infinity. 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.