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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 3, Pages 398–415
DOI: https://doi.org/10.4213/tmf8376 (Mi tmf8376) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Spectral properties of a thin layer with a doubly periodic family of thinning regions

S. A. Nazarov

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (545 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf8376
Abstract: We show that the spectrum of the Dirichlet problem for the Laplace operator in a layer with a doubly periodic structure has gaps and determine several characteristics of their location. The result is obtained by asymptotic analysis of a model spectral problem on the periodicity cell.
Keywords: Dirichlet problem in a doubly periodic layer, asymptotic behavior, eigenvalue localization, spectral gap.
Received: 04.06.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 3, Pages 343–359
DOI: https://doi.org/10.1007/s11232-013-0031-3
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. A. Nazarov, “Spectral properties of a thin layer with a doubly periodic family of thinning regions”, TMF, 174:3 (2013), 398–415; Theoret. and Math. Phys., 174:3 (2013), 343–359
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8376
  • https://www.mathnet.ru/eng/tmf/v174/i3/p398
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:69
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