Geodesic
On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 82-85 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Results on the convergence of minimizers and minimum values of integral and more general functionals $J_s\colon W^{1,p}(\Omega_s)\to\mathbb R$ on the sets $U_s(h_s)=\{v\in W^{1,p}(\Omega_s)\colon h_s(v)\leqslant 0\ \text{a.e.\ in }\Omega_s\}$, where $p>1$, $\{\Omega_s\}$ is a sequence of domains contained in a bounded domain $\Omega$ of $\mathbb R^n$ ($n\geqslant 2$), and $\{h_s\}$ is a sequence of functions on $\mathbb R$, are announced.
Keywords: integral functional, variational problem, implicit pointwise constraint, minimizer, minimum value
Mots-clés : $\Gamma$-convergence, variable domain. 
@article{FAA_2018_52_2_a7,
     author = {A. A. Kovalevsky},
     title = {On the {Convergence} of {Solutions} of {Variational} {Problems} with {Implicit} {Pointwise} {Constraints} in {Variable} {Domains}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {82--85},
     year = {2018},
     volume = {52},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a7/}
}
TY  - JOUR
AU  - A. A. Kovalevsky
TI  - On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2018
SP  - 82
EP  - 85
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a7/
LA  - ru
ID  - FAA_2018_52_2_a7
ER  - 
%0 Journal Article
%A A. A. Kovalevsky
%T On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2018
%P 82-85
%V 52
%N 2
%U http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a7/
%G ru
%F FAA_2018_52_2_a7
A. A. Kovalevsky. On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 82-85. http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a7/

[1] A. A. Kovalevskii, Sovremennyi analiz i ego prilozheniya. Sb. nauchn. trudov, Naukova dumka, Kiev, 1989, 62–70 | Zbl

[2] A. A. Kovalevskii, Tr. IMM UrO RAN, 22:1 (2016), 140–152 | MR

[3] E. Ya. Khruslov, Matem. sb., 106(148):4(8) (1978), 604–621 | MR | Zbl

[4] A. A. Kovalevskii, Nelinein. granichn. zadachi, 4 (1992), 29–39

[5] V. V. Zhikov, Izv. AN SSSR, Ser. matem., 47:5 (1983), 961–998 | MR | Zbl

[6] G. Dal Maso, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. (8), 74:2 (1983), 55–61 | MR | Zbl

[7] G. Dal Maso, Ann. Mat. Pura Appl. (4), 129:1 (1981), 327–366 | DOI | MR

[8] M. M. Vainberg, Variatsionnyi metod i metod monotonnykh operatorov v teorii nelineinykh uravnenii, Nauka, M., 1972 | MR

[9] K. Kuratovskii, Topologiya, v. 1, Mir, M., 1966 | MR