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Numerical methods and programming, 2009, Volume 10, Issue 1, Pages 83–93 (Mi vmp358)  
Вычислительные методы и приложения

Two-sided estimates for the eigenvalues of the Laplace operator with Dirichlet boundary conditions and their application to problems in the mathematical theory of waveguides

A. N. Bogolyubov, M. D. Malykh, A. A. Panin

Lomonosov Moscow State University, Faculty of Physics
Full-text PDF (1190 kB)
Abstract: Reliable two-sided algorithmically simple estimates for the eigenvalues of the Laplace operator in convex polygons with Dirichlet boundary conditions are obtained. These estimates are applied to the existence problem for the trapping modes of waveguides and to the problem of finding the frequency ranges for which the wave radiation occurs without resonance.
Keywords: eigenvalues of Laplace operator; two-sided estimates; trapping modes of waveguides; cut-off frequencies.
Document Type: Article
UDC: 519.632.6
Language: Russian
Citation: A. N. Bogolyubov, M. D. Malykh, A. A. Panin, “Two-sided estimates for the eigenvalues of the Laplace operator with Dirichlet boundary conditions and their application to problems in the mathematical theory of waveguides”, Num. Meth. Prog., 10:1 (2009), 83–93
Citation in format AMSBIB
\Bibitem{BogMalPan09}
\by A.~N.~Bogolyubov, M.~D.~Malykh, A.~A.~Panin
\paper Two-sided estimates for the eigenvalues of the Laplace operator with Dirichlet boundary conditions and their application to problems in the mathematical theory of waveguides
\jour Num. Meth. Prog.
\yr 2009
\vol 10
\issue 1
\pages 83--93
\mathnet{http://mi.mathnet.ru/vmp358}
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