Geodesic
Homogenization of the Variational Inequality Corresponding to a Problem with Rapidly Varying Boundary Conditions
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 538-549

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In the present paper, we investigate the asymptotic behavior of the solution of a variational inequality with one-sided constraints on $\varepsilon$-periodically located subsets $G_\varepsilon$ belonging to the boundary $\partial\Omega$ of the domain $\Omega\subset \mathbb R^3$. We construct a limit (homogenized) problem and prove the strong (in $H_1(\Omega)$) convergence of the solutions of the original inequality to the solution the limit nonlinear boundary-value problem as $\varepsilon\to0$ in the so-called critical case.
Keywords: variational inequality, rapidly varying boundary conditions, boundary homogenization, strong convergence, domain with periodically bounded subsets. 
@article{MZM_2007_82_4_a8,
     author = {M. N. Zubova and T. A. Shaposhnikova},
     title = {Homogenization of the {Variational} {Inequality} {Corresponding} to a {Problem} with {Rapidly} {Varying} {Boundary} {Conditions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {538--549},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a8/}
}
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M. N. Zubova; T. A. Shaposhnikova. Homogenization of the Variational Inequality Corresponding to a Problem with Rapidly Varying Boundary Conditions. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 538-549. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a8/