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Izvestiya: Mathematics, 2002, Volume 66, Issue 2, Pages 299–365
DOI: https://doi.org/10.1070/IM2002v066n02ABEH000380 (Mi im380) 		 
This article is cited in 117 scientific papers (total in 117 papers)

Homogenization of elasticity problems on singular structures

V. V. Zhikov

Vladimir State Pedagogical University
English version PDF (634 kB) Citations (117)
References:
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DOI: https://doi.org/10.1070/IM2002v066n02ABEH000380
Abstract: We consider homogenization theory on periodic networks, junctions and more general singular objects. We show that the homogenized problem typically has a “non-classical” character. This fact is a distinctive feature of homogenization of elasticity problems in contrast to scalar problems.
We investigate the properties of Sobolev spaces for various singular structures, prove a non-classical homogenization principle for singular periodic structures of general type and describe a “scaling effect” for model problems with two small geometrical parameters.
Received: 23.11.2000
Revised: 10.09.2001
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2002, Volume 66, Issue 2, Pages 81–148
DOI: https://doi.org/10.4213/im380
Bibliographic databases:
UDC: 517.9
MSC: 35B27
Language: English
Original paper language: Russian
Citation: V. V. Zhikov, “Homogenization of elasticity problems on singular structures”, Izv. RAN. Ser. Mat., 66:2 (2002), 81–148; Izv. Math., 66:2 (2002), 299–365
Citation in format AMSBIB
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\by V.~V.~Zhikov
\paper Homogenization of elasticity problems on singular structures
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 2
\pages 81--148
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\zmath{https://zbmath.org/?q=an:1043.35031}
\elib{https://elibrary.ru/item.asp?id=13802991}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 2
\pages 299--365
\crossref{https://doi.org/10.1070/IM2002v066n02ABEH000380}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748487201}
Linking options:
  • https://www.mathnet.ru/eng/im380
  • https://doi.org/10.1070/IM2002v066n02ABEH000380
  • https://www.mathnet.ru/eng/im/v66/i2/p81
    • This publication is cited in the following 117 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1248
    Russian version PDF:548
    English version PDF:26
    References:76
    First page:3
     
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