On $G$-compactness of a~class of nondivergence elliptic operators of second order
Izvestiya. Mathematics , Tome 19 (1982) no. 1, pp. 27-40.

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This paper introduces the concept of $G$-convergence for nondivergence elliptic operators of second order. It is proved that the class of operators subject to the natural ellipticity inequalities and to a certain “cone” condition (Cordes' condition) is compact in the $G$-topology. Bibliography: 14 titles.
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V. V. Zhikov; M. M. Sirazhudinov. On $G$-compactness of a~class of nondivergence elliptic operators of second order. Izvestiya. Mathematics , Tome 19 (1982) no. 1, pp. 27-40. http://geodesic.mathdoc.fr/item/IM2_1982_19_1_a2/

[1] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[2] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, t. I, Mir, M., 1977 | MR

[3] Spagnoto S., “Sul limite delle solutioni di problemi di Cauchy relativi all'equazione del calore”, Ann. Scuola Norm. Sup. Pisa, Cl. Sci., 21 (1967), 657–699 | MR

[4] Spagnolo S., “Sulla convergenza di solutioni di equazioni paraboliche ed ellittiche”, Ann. Scuola Norm. Sup. Pisa, Cl. Sci., 22 (1968), 577–597 | MR

[5] De Giorgi E., Spagnolo S., “Sulla convergenza degli integrali dell 'energia per operatori ellittici del 2 ordine”, Boll. Un. Mat. Ital., 8:4 (1973), 391–411 | MR | Zbl

[6] Zhikov V. V., Kozlov S. M., Oleinik O. A., Ngoan Kha Ten, “Usrednenie i $G$-skhodimost differentsialnykh operatorov”, Uspekhi matem. nauk, 34:5(209) (1979), 65–133 | MR | Zbl

[7] Aleksandrov A. D., “Usloviya edinstvennosti i otsenki resheniya zadachi Dirikhle”, Vestnik LGU, 1963, no. 13, 5–29 | MR | Zbl

[8] Kordes O. G., “O pervoi kraevoi zadache dlya kvazilineinykh differentsialnykh uravnenii bolee chem s dvumya peremennymi”, Matematika, 3:2 (1959), 75–107

[9] Krylov N. V., “O predelnom perekhode v parabolicheskikh uravneniyakh Bellmana”, Izv. AN SSSR. Ser. matem., 42:6 (1978), 1417–1425 | MR | Zbl

[10] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[11] Krylov N. V., “O printsipe maksimuma dlya nelineinykh parabolicheskikh i ellipticheskikh uravnenii”, Izv. AN SSSR. Ser. matem., 42:5 (1978), 1050–1062 | MR | Zbl

[12] Krylov N. V., “Ob odnom klasse nelineinykh uravnenii v prostranstve izmerimykh funktsii”, Matem. sb., 80:2 (1969), 253–265 | MR | Zbl

[13] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR

[14] Bers L., Dzhon F., Shekhter M., Uravneniya s chastnymi proizvodnymi, Mir, M., 1966 | MR | Zbl