Geodesic
Control of the shape of the domain in elliptic sistems and choice of the optimal domain in the Stokes problem
Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 165-175 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The author considers problems on choice of an optimal domain for which a solution of a system of elliptic equations depending on the shape of the domain delivers a minimum or maximum to some functional on the set of admissible domains (controls). Bibliography: 11 titles. 
@article{SM_1990_67_1_a9,
     author = {V. G. Litvinov},
     title = {Control of the~shape of the domain in elliptic sistems and choice of the~optimal domain in {the~Stokes} problem},
     journal = {Sbornik. Mathematics},
     pages = {165--175},
     year = {1990},
     volume = {67},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_67_1_a9/}
}
TY  - JOUR
AU  - V. G. Litvinov
TI  - Control of the shape of the domain in elliptic sistems and choice of the optimal domain in the Stokes problem
JO  - Sbornik. Mathematics
PY  - 1990
SP  - 165
EP  - 175
VL  - 67
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1990_67_1_a9/
LA  - en
ID  - SM_1990_67_1_a9
ER  - 
%0 Journal Article
%A V. G. Litvinov
%T Control of the shape of the domain in elliptic sistems and choice of the optimal domain in the Stokes problem
%J Sbornik. Mathematics
%D 1990
%P 165-175
%V 67
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1990_67_1_a9/
%G en
%F SM_1990_67_1_a9
V. G. Litvinov. Control of the shape of the domain in elliptic sistems and choice of the optimal domain in the Stokes problem. Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 165-175. http://geodesic.mathdoc.fr/item/SM_1990_67_1_a9/

[1] Banichuk N. V., Optimizatsiya form uprugikh tel, Nauka, M., 1980 | MR

[2] Sea Zh., “Chislennyi metod poiska optimalnoi oblasti”, Vychislitelnye metody v matematicheskoi fizike, geofizike i optimalnom upravlenii, Nauka, Novosibirsk, 1978, 63–73

[3] Litvinov V. G., Optimizatsiya v ellipticheskikh granichnykh zadachakh s prilozheniyami k mekhanike, Nauka, M., 1987 | MR

[4] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

[5] Ivanov L. A., Katko L. A., Krein S. G., “Kraevye zadachi v peremennykh oblastyakh”, Differentsialnye uravneniya i ikh primenenie, 19, Vilnyus, 1977

[6] Krein S. G., “Povedenie reshenii ellipticheskikh zadach pri variatsii oblasti”, Studia Mathematica, 31:4 (1968), 411–424 | MR | Zbl

[7] Murat F., Simon J., “Etude de problemes d'optimal desigh”, Lect. Notes in computer Sci., 41 (1976), 54–62 | Zbl

[8] Ladyzhenskaya O. A., Solonnikov V. A., “O nekotorykh zadachakh vektornogo analiza i obobschennykh postanovkakh kraevykh zadach dlya uravnenii Nave–Stoksa”, Zap. nauch. semin. LOMI, 59 (1976), 81–116 | Zbl

[9] Girault V., Raviart P.-A., Finite element approximation of the Navier–Stokes equations, Springer-Verlag, Berlin, Heidelberg, New York, 1981 | MR | Zbl

[10] Shvarts L., Analiz, t. I, Mir, M., 1972

[11] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl