Spectra of Dirichlet Laplacian in 3-dimensional polyhedral layers
Spectral Theory
2023-05-16 v2
Abstract
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.
Cite
@article{arxiv.2304.10575,
title = {Spectra of Dirichlet Laplacian in 3-dimensional polyhedral layers},
author = {Fedor Bakharev and Sergey Matveenko},
journal= {arXiv preprint arXiv:2304.10575},
year = {2023}
}
Comments
Some misprints are fixed