Geodesic
The solvability of extremal problems for Poisson equation and Stokes system
Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 164-170.

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One consider the extremal problems for Poisson equation and Stokes system which are to minimize the $L^2$-difference solution from given function. The sufficient conditions of solvability in the Sobolev space $H^1$ are obtained. It is showed that these conditions are necessary in some cases. 
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A. A. Illarionov. The solvability of extremal problems for Poisson equation and Stokes system. Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 164-170. http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a2/

[1] G. V. Alekseev, V. V. Malykin, “Chislennoe issledovanie statsionarnykh ekstremalnykh zadach dlya dvumernykh uravnenii vyazkoi zhidkosti”, Vychisl. tekhnologii, 2:5 (1993) | Zbl

[2] G. V. Alekseev, V. V. Malikin, “Numerical analysis of optimal control problems for Navier – Stokes equations”, CFD, 3:1 (1994)

[3] A. V. Fursikov, Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999

[4] A. Yu. Chebotarev, “Granichnye ekstremalnye zadachi dinamiki vyazkoi neszhimaemoi zhidkosti”, Sib. mat. zhurn., 34:5 (1993), 202–213 | MR | Zbl

[5] A. Yu. Chebotarev, “Printsip maksimuma v zadache granichnogo upravleniya techeniem vyazkoi zhidkosti”, Sib. mat. zhurn., 34:6 (1993), 189–197 | MR | Zbl

[6] A. Yu. Chebotarev, “Normalnye resheniya kraevykh zadach dlya statsionarnykh sistem tipa Nave – Stoksa”, Sib. mat. zhurn., 36:5 (1995), 934–942 | MR | Zbl

[7] A. A. Illarionov, “Asimptotika reshenii zadachi optimalnogo upravleniya dlya statsionarnykh uravnenii Nave – Stoksa”, Zh. vychisl. matem. i matem. fiz., 40:7 (2000), 1061–1070 | MR

[8] A. A. Illarionov, “Optimalnoe granichnoe upravlenie statsionarnym techeniem vyazkoi neodnorodnoi neszhimaemoi zhidkosti”, Matem. zametki, 69:5 (2001), 666–678 | MR | Zbl

[9] A. A. Illarionov, “Ob asimptotike reshenii zadachi optimalnogo upravleniya dlya statsionarnykh uravnenii Nave – Stoksa”, Zh. vychisl. matem. i matem. fiz., 41:7 (2001), 1045–1056 | MR | Zbl

[10] G. V. Alekseev, “Razreshimost statsionarnykh zadach granichnogo upravleniya dlya uravnenii teplovoi konvektsii”, Sib. mat. zhurn., 39:5 (1998), 982–998 | MR | Zbl

[11] V. A. Solonnikov, “Ob obschikh kraevykh zadachakh dlya sistem, ellipticheskikh v smysle A. Daglisa – L. Nirenberga. II”, Trudy MIAN SSSR, XCII, 1966, 233–297 | MR

[12] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[13] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970 | MR

[14] S. Agmon, A. Duglis, L. Nirenberg, Otsenki vblizi granitsy reshenii ellipticheskikh uravnenii v chastnykh proizvodnykh pri obschikh granichnykh usloviyakh, Izd-vo inostr. lit., M., 1962, 205 pp.

[15] A. A. Illarionov, “O razreshimosti kraevykh zadach dlya statsionarnykh uravnenii Nave-Stoksa”, Dalnevostochnyi matem. zhurn., 2:1 (2001), 16–36