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Mat. Sb., 2005, Volume 196, Number 4, Pages 79–98 (Mi msb1286)  

This article is cited in 5 scientific papers (total in 5 papers)

Homogenization of variational inequalities for obstacle problems

G. V. Sandrakov

National Technical University of Ukraine "Kiev Polytechnic Institute"

Abstract: Results on the convergence of solutions of variational inequalities for obstacle problems are proved. The variational inequalities are defined by a non-linear monotone operator of the second order with periodic rapidly oscillating coefficients and a sequence of functions characterizing the obstacles. Two-scale and macroscale (homogenized) limiting variational inequalities are obtained. Derivation methods for such inequalities are presented. Connections between the limiting variational inequalities and two-scale and macroscale minimization problems are established in the case of potential operators.

DOI: https://doi.org/10.4213/sm1286

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English version:
Sbornik: Mathematics, 2005, 196:4, 541–560

Bibliographic databases:

UDC: 517.95
MSC: 35B27
Received: 25.03.2004 and 31.01.2005

Citation: G. V. Sandrakov, “Homogenization of variational inequalities for obstacle problems”, Mat. Sb., 196:4 (2005), 79–98; Sb. Math., 196:4 (2005), 541–560

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm1286
  • http://mi.mathnet.ru/eng/msb/v196/i4/p79

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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. G. V. Sandrakov, “Homogenization of nonlinear equations and variational inequalities with obstacles”, Dokl. Math., 73:2 (2006), 178–181  mathnet  crossref  mathscinet  zmath  isi  elib
    2. G. V. Sandrakov, “Homogenization of variational inequalities and equations defined by pseudomonotone operators”, Sb. Math., 199:1 (2008), 67–98  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Shaposhnikova T.A., Zubova M.N., “Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain”, Netw. Heterog. Media, 3:3 (2008), 675–689  crossref  mathscinet  zmath  isi  elib
    4. Marcon D., Rodrigues J.F., Teymurazyan R., “Homogenization of Obstacle Problems in Orlicz-Sobolev Spaces”, Port Math., 75:3-4 (2018), 267–283  crossref  mathscinet  zmath  isi
    5. Tan W.Ch., Viet Ha Hoang, “Sparse Tensor Product Finite Element Method For Nonlinear Multiscale Variational Inequalities of Monotone Type”, IMA J. Numer. Anal., 40:3 (2020), 1875–1907  crossref  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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