Spectral analysis in broken sheared waveguides

2022/03/30 by Diana C. S. Bello, Bello, Diana C. S., Alessandra A. Verri +1 · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #Mathematical Analysis and Transform Methods #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2203.16591

Abstract

Let Ω⊂ \mathbb R³ 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 R³. We prove that the discrete spectrum of the Dirichlet Laplacian operator in Ω is non-empty and finite. Furthermore, we show a particular geometry for Ω which implies that the total multiplicity of the discrete spectrum is equals 1.

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