Homogenization of the variational inequality corresponding to a problem with rapidly varying boundary conditions
M. N. Zubova, Т. А. Шапошникова · Mathematical Notes · 2007
In the present paper, we investigate the asymptotic behavior of the solution of a variational inequality with one-sided constraints on ɛ-periodically located subsets G ε belonging to the boundary ∂Ω of the domain Ω ⊂ ℝ3. We construct a limit (homogenized) problem and prove the strong (in H 1(Ω)) convergence of the solutions of the original inequality to the solution the limit nonlinear boundary-value problem as ɛ → 0 in the so-called critical case.