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
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.
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Izvestiya: Mathematics, 1997, 61:1, 69–88
MSC: Primary 35B27, 35J65; Secondary 73B27
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
\by V.~V.~Zhikov, M.~E.~Rychago
\paper Homogenization of non-linear second-order elliptic equations in perforated domains
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
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S. E. Pastukhova, “On homogenization of a variational inequality for an elastic body with periodically distributed fissures”, Sb. Math., 191:2 (2000), 291–306
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
G. V. Sandrakov, “Homogenization of variational inequalities for non-linear diffusion problems in perforated domains”, Izv. Math., 69:5 (2005), 1035–1059
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
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