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Spectral analysis in broken sheared waveguides
Authors
Diana C. S. Bello
Alessandra A. Verri
Publication date
17 July 2022
Publisher
View
on
arXiv
Abstract
Let
Ω
⊂
R
3
\Omega \subset \mathbb R^3
Ω
⊂
R
3
be a broken sheared waveguide, i.e., it is built by translating a cross-section in a constant direction along a broken line in
R
3
\mathbb R^3
R
3
. We prove that the discrete spectrum of the Dirichlet Laplacian operator in
Ω
\Omega
Ω
is non-empty and finite. Furthermore, we show a particular geometry for
Ω
\Omega
Ω
which implies that the total multiplicity of the discrete spectrum is equals 1.Comment: In this version, we add a result which shows a particular geometry for
Ω
\Omega
Ω
which implies that the total multiplicity of the discrete spectrum of the operator is equals
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Last time updated on 24/04/2022