Spectra of Dirichlet Laplacian in 3-dimensional polyhedral layers

The structure of the spectrum of the three-dimensional Dirichlet Laplacian in the 3D polyhedral layer of fixed width is studied. It appears that the essential spectrum is defined by the smallest dihedral angle that forms the boundary of the layer while the discrete spectrum is always finite. An exam...

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Bibliographic Details
Published in:arXiv.org 2023-05
Main Authors: Bakharev, Fedor, Matveenko, Sergey
Format: Article
Language:English
Subjects:
Dihedral angle
Dirichlet problem
Online Access:Get full text
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Summary:The structure of the spectrum of the three-dimensional Dirichlet Laplacian in the 3D polyhedral layer of fixed width is studied. It appears that the essential spectrum is defined by the smallest dihedral angle that forms the boundary of the layer while the discrete spectrum is always finite. An example of a layer with the empty discrete spectrum is constructed. The spectrum is proved to be nonempty in regular polyhedral layer.
ISSN:2331-8422