弯曲管中光谱阈值的下界

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-05-13 DOI:10.1098/rspa.2004.1356

P. Exner, P. Freitas, D. Krejčiřík

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引用次数: 27

摘要

考虑任意截面的弯曲管中的拉普拉斯算子在任意维欧几里得空间中沿曲线与Frenet框架一起旋转，同时满足柱面上的Dirichlet边界条件和管端处的Neumann条件。我们证明了拉普拉斯算子的谱阈值是由管的几何形状决定的环面上狄利克雷拉普拉斯算子的最低特征值从下估计出来的。

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A lower bound to the spectral threshold in curved tubes

We consider the Laplacian in curved tubes of arbitrary cross–section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.

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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

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期刊介绍： Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.