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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)
References:
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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
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  • https://www.mathnet.ru/eng/tmf8376
  • https://doi.org/10.4213/tmf8376
  • https://www.mathnet.ru/eng/tmf/v174/i3/p398
    • This publication is cited in the following 9 articles:
    1. D. B. Davletov, O. B. Davletov, R. R. Davletova, A. A. Ershov, “O sobstvennykh elementakh dvumernoi kraevoi zadachi tipa Steklova dlya operatora Lame”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:1 (2023), 54–65  mathnet  crossref  mathscinet
    2. Bakharev F.L., Matveenko S.G., “Localization of Eigenfunctions in a Narrow Kirchhoff Plate”, Russ. J. Math. Phys., 28:2 (2021), 156–178  crossref  mathscinet  isi
    3. S. A. Nazarov, “Discrete spectrum of cranked quantum and elastic waveguides”, Comput. Math. Math. Phys., 56:5 (2016), 864–880  mathnet  crossref  crossref  isi  elib
    4. Nazarov S.A., Perez E., Taskinen J., “Localization effect for Dirichlet eigenfunctions in thin non-smooth domains”, Trans. Am. Math. Soc., 368:7 (2016), 4787–4829  crossref  mathscinet  zmath  isi  scopus
    5. S. A. Nazarov, “Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube”, Trans. Moscow Math. Soc., 76:1 (2015), 1–53  mathnet  crossref  elib
    6. S. A. Nazarov, “Eigenmodes of a thin elastic layer between periodic rigid profiles”, Comput. Math. Math. Phys., 55:10 (2015), 1684–1697  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Nazarov S.A., “Asymptotics of the natural oscillations of a thin elastic gasket between absolutely rigid profiles”, Pmm-J. Appl. Math. Mech., 79:6 (2015), 577–586  crossref  mathscinet  isi  scopus
    8. S. A. Nazarov, “Localization of longitudinal and transverse oscillations in a thin curved elastic gasket”, Dokl. Phys., 60:10 (2015), 446  crossref
    9. S. A. Nazarov, “Asymptotics of eigenvalues of the Dirichlet problem in a skewed T-shaped waveguide”, Comput. Math. Math. Phys., 54:5 (2014), 793–814  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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