剪切波导断裂的谱分析
Spectral analysis in broken sheared waveguides
摘要：
假设$Ω\subset \mathbb R^3$是断裂的剪切波导，即，它是通过沿着$\mathbb R^3$中的折线在恒定方向上平移横截面来构建的。我们证明了$Ω$中Dirichlet Laplacian算子的离散谱是非空的和有限的.此外，我们显示了一个特殊的几何$Ω$，这意味着总的多重性的离散谱是等于1。
英文摘要：
Let $Ω\subset \mathbb R^3$ 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 $Ω$ 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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