The discrete spectrum of cross-shaped waveguides

Bakharev, F.; Matveenko, S.; Nazarov, S.

doi:10.1090/spmj/1444

The discrete spectrum of cross-shaped waveguides
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by F. L. Bakharev, S. G. Matveenko and S. A. Nazarov
Translated by: A. Plotkin

St. Petersburg Math. J. 28 (2017), 171-180

DOI: https://doi.org/10.1090/spmj/1444

Published electronically: February 15, 2017

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Abstract:

The discrete spectrum of the Dirichlet problem for the Laplace operator on the union of two circular unit cylinders whose axes intersect at the right angle consists of a single eigenvalue. For the threshold value of the spectral parameter, this problem has no bounded solutions. When the angle between the axes reduces, the multiplicity of the discrete spectrum grows unboundedly.

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