Maxwell operator in a cylinder with coefficients that do not depend on the longitudinal variable
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N. Filonov
Translated by: the author - St. Petersburg Math. J. 30 (2019), 545-572
- DOI: https://doi.org/10.1090/spmj/1558
- Published electronically: April 12, 2019
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Abstract:
The Maxwell operator in a 3-dimensional cylinder with Lipschitz cross-section is considered. The coefficients are assumed to be independent of the longitudinal variable. The spectrum of the operator is shown to be absolutely continuous. If the cross-section of the cylinder is multiply connected, then the spectrum fills the real axes. If the cross-section is simply connected, then the spectrum has one gap centered at the origin.References
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Bibliographic Information
- N. Filonov
- Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia; and St. Petersburg State University, University emb. 7/9, St. Petersburg 199034, Russia
- MR Author ID: 609754
- Email: filonov@pdmi.ras.ru
- Received by editor(s): October 28, 2017
- Published electronically: April 12, 2019
- Additional Notes: This research was supported by Russian Science Foundation, project no. 17-11-01069
- © Copyright 2019 American Mathematical Society
- Journal: St. Petersburg Math. J. 30 (2019), 545-572
- MSC (2010): Primary 35Q61
- DOI: https://doi.org/10.1090/spmj/1558
- MathSciNet review: 3812006
Dedicated: To the memory of M. Z. Solomjak