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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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