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Izvestiya: Mathematics, 1997, Volume 61, Issue 1, Pages 69–88
DOI: https://doi.org/10.1070/IM1997v061n01ABEH000105 (Mi im105) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Homogenization of non-linear second-order elliptic equations in perforated domains

V. V. Zhikova, M. E. Rychago

a Vladimir State Pedagogical University
English version PDF (243 kB) Citations (11)
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DOI: https://doi.org/10.1070/IM1997v061n01ABEH000105
Abstract: The classical homogenization method of elliptic boundary value problems is based on the continuation of a solution, given in a perforated domain, to the entire initial domain. This method requires substantial restrictions on the perforated domain (the “strong connectedness” condition). In this paper we propose a new approach, which does not use the continuation technique. Here the “strong connectedness” is replaced by the usual connectedness.
Received: 10.07.1995
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1997, Volume 61, Issue 1, Pages 69–88
DOI: https://doi.org/10.4213/im105
Bibliographic databases:
MSC: Primary 35B27, 35J65; Secondary 73B27
Language: English
Original paper language: Russian
Citation: V. V. Zhikov, M. E. Rychago, “Homogenization of non-linear second-order elliptic equations in perforated domains”, Izv. RAN. Ser. Mat., 61:1 (1997), 69–88; Izv. Math., 61:1 (1997), 69–88
Citation in format AMSBIB
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\pages 69--88
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    • This publication is cited in the following 11 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:569
    Russian version PDF:231
    English version PDF:22
    References:82
    First page:1
     
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