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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 1, Pages 203–240 (Mi izv8286)  

This article is cited in 3 scientific papers (total in 3 papers)

Homogenization of spectral problems with singular perturbation of the Steklov condition

A. G. Chechkina

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We consider spectral problems with Dirichlet- and Steklov-type conditions on alternating small pieces of the boundary. We study the behaviour of the eigenfunctions of such problems as the small parameter (describing the size of the boundary microstructure) tends to zero. Using general methods of Oleinik, Yosifian and Shamaev, we give bounds for the deviation of these eigenfunctions from those of the limiting problem in various cases.

Keywords: spectral problem, Steklov problem, homogenization, asymptotics.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.W02.16.7461-
This paper was written with the partial financial support of the President's programme ‘Support of Leading Scientific Schools of Russia’ (grant no. 14.W02.16.7461-NSh).


DOI: https://doi.org/10.4213/im8286

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English version:
Izvestiya: Mathematics, 2017, 81:1, 199–236

Bibliographic databases:

UDC: 517.9
MSC: 35B25, 35B27, 35J25, 35P10, 35P15
Received: 18.08.2014
Revised: 18.10.2015

Citation: A. G. Chechkina, “Homogenization of spectral problems with singular perturbation of the Steklov condition”, Izv. RAN. Ser. Mat., 81:1 (2017), 203–240; Izv. Math., 81:1 (2017), 199–236

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Chechkina A.G., “Estimate of the spectrum deviation of the singularly perturbed Steklov problem”, Dokl. Math., 96:2 (2017), 510–513  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. D. Gómez, S. A. Nazarov, M. E. Pérez, “Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity”, Z. Angew. Math. Phys., 69:2 (2018), 35, 23 pp.  crossref  mathscinet  zmath  isi  scopus
    3. Chechkina A.G., D'Apice C., De Maio U., “Rate of Convergence of Eigenvalues to Singularly Perturbed Steklov-Type Problem For Elasticity System”, Appl. Anal., 98:1-2, SI (2019), 32–44  crossref  mathscinet  isi  scopus
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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