Geodesic
Boundary-value problems for general elliptic systems in the plane
Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 1031-1068.

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We consider boundary-value problems for general elliptic systems in a bounded multiply connected domain with a smooth boundary in the plane. This includes boundary-value problems for homogeneous elliptic systems and for systems elliptic in the sense of Petrovskii or Douglis–Nirenberg. The systems under consideration need not be properly elliptic. We obtain necessary and sufficient conditions for the system to be Noetherian and give index formulae with applications to geometry and hydrodynamics. 
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M. M. Sirazhudinov. Boundary-value problems for general elliptic systems in the plane. Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 1031-1068. http://geodesic.mathdoc.fr/item/IM2_1997_61_5_a5/

[1] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR | Zbl

[2] Vekua I. N., Obobschennye analiticheskie funktsii, 2-e izd., pererab., Nauka, M., 1988 | MR | Zbl

[3] Volpert A. I., “Ob indekse i normalnoi razreshimosti granichnykh zadach dlya ellipticheskikh sistem na ploskosti”, Tr. MMO, 10, URSS, M., 1961, 41–87 | MR | Zbl

[4] Zhura N. A., “Kraevye zadachi tipa Bitsadze–Samarskogo dlya ellipticheskikh v smysle Duglisa–Nirenberga sistem”, Differents. uravn., 28:1 (1992), 81–91 | MR

[5] Soldatov A. P., “Metod teorii funktsii v kraevykh zadachakh na ploskosti. 1: Gladkii sluchai”, Izv. AN. Ser. matem., 55:5 (1991), 1070–1100 | MR | Zbl

[6] Sirazhudinov M. M., “O zadache Rimana–Gilberta dlya ellipticheskikh sistem pervogo poryadka v mnogosvyaznoi oblasti”, Matem. sb., 184:11 (1993), 39–62 | MR | Zbl

[7] Solonnikov V. A., “Ob obschikh kraevykh zadachakh dlya sistem, ellipticheskikh v smysle A. Duglisa–L. Nirenberga. II”, Tr. MIAN, 92, Nauka, M., 1966, 233–297

[8] Vinogradov V. S., “Granichnaya zadacha dlya ellipticheskoi sistemy pervogo poryadka na ploskosti”, Differents. uravn., 7:8 (1971), 1440–1448 | MR | Zbl

[9] Volpert A. I., “Normalnaya razreshimost granichnykh zadach dlya ellipticheskikh sistem differentsialnykh uravnenii na ploskosti”, Teor. i prikl. matem., 1958, no. 1, 28–57 | MR

[10] Saks R. S., Kraevye zadachi dlya ellipticheskikh sistem differentsialnykh uravnenii, Izd-vo NGU, Novosibirsk, 1975

[11] Boyarskii V. V., “Teoriya obobschennogo analiticheskogo vektora”, Ann. Polon. Mathem., 17:3 (1968), 281–320

[12] Soldatov A. P., “Obschaya kraevaya zadacha $(k-1)$-go poryadka dlya ellipticheskikh uravnenii”, DAN SSSR, 311:1 (1990), 39–43 | Zbl

[13] Presdorf Z., Nekotorye klassy singulyarnykh uravnenii, Mir, M., 1979 | MR

[14] Boyarskii B. V., Nekotorye kraevye zadachi dlya uravnenii ellipticheskogo tipa na ploskosti, Dis. ...kand. fiz.-mat. nauk, MGU, M., 1955

[15] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka, M., 1988

[16] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, GIFML, M., 1961

[17] Belonosov S. M., Chernous K. A., Kraevye zadachi dlya uravnenii Nave–Stoksa, Nauka, M., 1985 | MR

[18] Solonnikov V. A., “Razreshimost zadach o dvizhenii vyazkoi neszhimaemoi zhidkosti, ogranichennoi svobodnoi poverkhnostyu”, Nekotorye problemy gazovoi dinamiki, Sb. nauchnykh trudov, no. XXII, Izd-vo in-ta gidrodinamiki SO AN SSSR, Novosibirsk, 1975, 182–197