Discrete spectrum of cranked, branching, and periodic waveguides
Discrete spectrum of cranked, branching, and periodic waveguides
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曲柄波导、分支波导和周期波导的离散频谱
DOI：
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发表时间：
2012
期刊：
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通讯作者：
S. Nazarov
中科院分区：
文献类型：
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作者：
S. Nazarov
本文将变分方法应用于具有圆柱出口或周期出口至无穷远的平面或多维域（波导）中具有混合边界条件和Dirichlet条件的拉普拉斯算子谱的研究。全面讨论了等宽平面波导的曲柄波导、折弯波导、顺弯波导和分支波导。对于它们，建立了特征值低于连续谱阈值的存在性。对于多维曲曲和分支波导，以及一些周期波导，也得到了类似的结果。提出了几个悬而未决的问题；特别地，他们关注的问题与诺依曼边界条件，完全多重的离散频谱，和平面波导的分段常数边界。§
The variational method is applied to the study of the spectrum of the Laplace operator with mixed boundary conditions and with Dirichlet conditions in planar or multidimensional domains (waveguides) with cylindrical or periodic exits to infinity. The planar waveguides of constant width are discussed completely, such as cranked, broken, smoothly bent, or branching waveguides. For them, the existence of eigenvalues below the continuous spectrum threshold is established. A similar result is obtained for the multidimensional cranked and branching waveguides, and also for some periodic ones. Several open questions are stated; in particular, they concern problems with Neumann boundary conditions, full multiplicity of the discrete spectrum, and planar waveguides with piecewise constant boundary. §