1. Spectral analysis in broken sheared waveguides
- Author
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Bello, Diana C. S. and Verri, Alessandra A.
- Subjects
Mathematics - Spectral Theory - Abstract
Let $\Omega \subset \mathbb R^3$ be a broken sheared waveguide, i.e., it is built by translating a cross-section in a constant direction along a broken line in $\mathbb R^3$. We prove that the discrete spectrum of the Dirichlet Laplacian operator in $\Omega$ is non-empty and finite. Furthermore, we show a particular geometry for $\Omega$ 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 $\Omega$ which implies that the total multiplicity of the discrete spectrum of the operator is equals 1
- Published
- 2022