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Homogenization of some variational inequalities with restrictions on subsets ɛ-periodically located along the domain boundary

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Abstract

In this paper some problems concerning homogenization of variational inequalities for the Laplace operator and the biharmonic operator with restrictions on subsets ɛ-periodically located along the domain boundary are studied (ɛ is a small parameter). These subsets are collections of balls of radius a ɛ a. An asymptotics of solutions is obtained in the so-called critical case characterized by a specific relation between the period ɛ and the value a ɛ. Strong convergence of solutions and their gradients is also established.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    M. N. Zubova & T. A. Shaposhnikova

Authors
  1. M. N. Zubova
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  2. T. A. Shaposhnikova
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Additional information

Original Russian Text © M.N. Zubova, T.A. Shaposhnikova, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 2, pp. 26–37.

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Zubova, M.N., Shaposhnikova, T.A. Homogenization of some variational inequalities with restrictions on subsets ɛ-periodically located along the domain boundary. Moscow Univ. Math. Bull. 62, 67–77 (2007). https://doi.org/10.3103/S0027132207020052

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  • DOI: https://doi.org/10.3103/S0027132207020052

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