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Spectrum asymptotics for one ``nonsmooth'' variational problem with solvable constraint


Authors: A. B. Alekseev, M. Sh. Birman and N. D. Filonov
Translated by: N. D. Filonov
Original publication: Algebra i Analiz, tom 18 (2006), nomer 5.
Journal: St. Petersburg Math. J. 18 (2007), 681-697
MSC (2000): Primary 35P20
DOI: https://doi.org/10.1090/S1061-0022-07-00968-5
Published electronically: August 9, 2007
MathSciNet review: 2301038
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Abstract | References | Similar Articles | Additional Information

Abstract: In a previous paper by Birman and Filonov, the spectrum of the Maxwell operator with nonsmooth coefficients in Lipschitz domains was investigated. The claim that its eigenvalues obey the Weyl asymptotics was proved up to a statement about the spectrum of an auxiliary problem with constraint. The proof of that statement is given in the present paper.


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Additional Information

A. B. Alekseev
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia

M. Sh. Birman
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia
Email: mbirman@list.ru

N. D. Filonov
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia
Email: laugre@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-07-00968-5
Keywords: Weyl spectrum asymptotics, resonator with perfectly conductive boundary, spectrum of the quotient of quadratic forms, problem with constraint
Received by editor(s): August 4, 2006
Published electronically: August 9, 2007
Article copyright: © Copyright 2007 American Mathematical Society