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Weyl asymptotics for the spectrum of the Maxwell operator in Lipschitz domains of arbitrary dimension


Author: N. Filonov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 25 (2013), nomer 1.
Journal: St. Petersburg Math. J. 25 (2014), 117-149
MSC (2010): Primary 35P20
DOI: https://doi.org/10.1090/S1061-0022-2013-01282-9
Published electronically: November 20, 2013
MathSciNet review: 3113431
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Abstract: The eigenvalues of the multidimensional Maxwell operator in a domain in the Euclidean space are shown to obey the Weyl asymptotics.


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Additional Information

N. Filonov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023; St. Petersburg State University, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg 198504, Russia
Email: filonov@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-2013-01282-9
Keywords: Maxwell operator, Weyl spectral asymptotics, domains with Lipschitz boundary, differential forms, ratios of quadratic forms
Received by editor(s): September 21, 2012
Published electronically: November 20, 2013
Additional Notes: Supported by the RFBR grant 11-01-00458-a and by the grant NSh-357.2012.1
Dedicated: To the memory of M. Sh. Birman
Article copyright: © Copyright 2013 American Mathematical Society