Spectral analysis in broken sheared waveguides

Diana C. S. Bello; Alessandra A. Verri

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arXiv · 2203.16591

Spectral analysis in broken sheared waveguides

Diana C. S. Bello·Alessandra A. Verri

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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.

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BibTeX RIS

Diana C. S. Bello, Alessandra A. Verri. 2022-03-30. Spectral analysis in broken sheared waveguides. https://arxiv.org/abs/2203.16591

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