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Algebra i Analiz, 2020, Volume 32, Issue 1, Pages 187–207 (Mi aa1686)  

This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

Maxwell operator in a cylinder with coefficients that do not depend on the cross-sectional variables

N. D. Filonovab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
Full-text PDF (256 kB) Citations (1)
References:
Abstract: The Maxwell operator is studied in a three-dimensional cylinder whose cross-section is a simply connected bounded domain with Lipschitz boundary. It is assumed that the coefficients of the operator are scalar functions depending on the longitudinal variable only. We show that the square of such an operator is unitarily equivalent to the orthogonal sum of four scalar elliptic operators of second order. If the coefficients are periodic along the axis of the cylinder, the spectrum of the Maxwell operator is absolutely continuous.
Keywords: Maxwell operator, simply connected cylinder, absolute continuity of the spectrum.
Funding agency Grant number
Russian Science Foundation 17-11-01069
This work was supported by Russian Science Foundation, grant 17-11-01069.
Received: 31.08.2019
English version:
St. Petersburg Mathematical Journal, 2021, Volume 32, Issue 1, Pages 139–154
DOI: https://doi.org/10.1090/spmj/1641
Bibliographic databases:
Document Type: Article
MSC: 35Q61
Language: Russian
Citation: N. D. Filonov, “Maxwell operator in a cylinder with coefficients that do not depend on the cross-sectional variables”, Algebra i Analiz, 32:1 (2020), 187–207; St. Petersburg Math. J., 32:1 (2021), 139–154
Citation in format AMSBIB
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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