论文标题
破碎的剪切波导中的光谱分析
Spectral analysis in broken sheared waveguides
论文作者
论文摘要
令$ω\ subset \ mathbb r^3 $为破碎的剪切波导，即，它是通过沿$ \ mathbb r^3 $的损坏线沿恒定方向转换横截面来构建的。我们证明，$ω$的Dirichlet Laplacian操作员的离散频谱是非空的和有限的。此外，我们显示了$ω$的特定几何形状，这意味着离散频谱的总多样性等于1。
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.
