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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 1, Pages 69–88 (Mi izv105)  

This article is cited in 4 scientific papers (total in 4 papers)

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

V. V. Zhikova, M. E. Rychago

a Vladimir State Pedagogical University

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.

DOI: https://doi.org/10.4213/im105

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English version:
Izvestiya: Mathematics, 1997, 61:1, 69–88

Bibliographic databases:

MSC: Primary 35B27, 35J65; Secondary 73B27
Received: 10.07.1995

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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\paper Homogenization of non-linear second-order elliptic equations in perforated domains
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. E. Pastukhova, “On homogenization of a variational inequality for an elastic body with periodically distributed fissures”, Sb. Math., 191:2 (2000), 291–306  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. E. Pastukhova, “Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain”, Sb. Math., 192:2 (2001), 245–260  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. G. V. Sandrakov, “Homogenization of variational inequalities for non-linear diffusion problems in perforated domains”, Izv. Math., 69:5 (2005), 1035–1059  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Mel'nyk, TA, “Asymptotic analysis of a boundary-value problem with nonlinear multiphase boundary interactions in a perforated domain”, Ukrainian Mathematical Journal, 61:4 (2009), 592  crossref  mathscinet  zmath  isi  scopus  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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