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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2007},
     volume = {82},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a8/}
}
TY  - JOUR
AU  - M. N. Zubova
AU  - T. A. Shaposhnikova
TI  - Homogenization of the Variational Inequality Corresponding to a Problem with Rapidly Varying Boundary Conditions
JO  - Matematičeskie zametki
PY  - 2007
SP  - 538
EP  - 549
VL  - 82
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a8/
LA  - ru
ID  - MZM_2007_82_4_a8
ER  - 
%0 Journal Article
%A M. N. Zubova
%A T. A. Shaposhnikova
%T Homogenization of the Variational Inequality Corresponding to a Problem with Rapidly Varying Boundary Conditions
%J Matematičeskie zametki
%D 2007
%P 538-549
%V 82
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a8/
%G ru
%F MZM_2007_82_4_a8
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/

[1] A. Damlamian, Li Ta-Tsien, “Boundary homogenization for elliptic problems”, J. Math. Pures Appl. (9), 66:4 (1987), 351–361 | MR | Zbl

[2] G. A. Chechkin, “Usrednenie kraevykh zadach s singulyarnym vozmuscheniem granichnykh uslovii”, Matem. sb., 184:6 (1993), 99–150 | MR | Zbl

[3] R. R. Gadylshin, “O kraevoi zadache dlya laplasiana s bystro menyayuschimisya granichnymi usloviyami”, Dokl. RAN, 362:4 (1998), 456–459 | MR | Zbl

[4] D. I. Borisov, “On a model boundary value problem for Laplacian with frequently alternating type of boundary condition”, Asymptot. Anal., 35:1 (2003), 1–26 | MR | Zbl

[5] I. Ekland, R. Temam, Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979 | MR | Zbl