Geodesic
Elliptic boundary value problems with periodic coefficients in a~cylinder
Izvestiya. Mathematics , Tome 18 (1982) no. 1, pp. 89-98.

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In a domain with periodically varying cross-section, this paper studies boundary value problems, elliptic in the Douglis–Nirenberg sense, in which the coefficients are periodic functions with the same period. Necessary and sufficient conditions for the unique solvability of these problems in function spaces with weighted norms are proved, and theorems on the Noether property and on the asymptotics of the solutions of boundary value problems with exponentially small perturbations of the coefficients are adduced. Bibliography: 15 titles. 
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S. A. Nazarov. Elliptic boundary value problems with periodic coefficients in a~cylinder. Izvestiya. Mathematics , Tome 18 (1982) no. 1, pp. 89-98. http://geodesic.mathdoc.fr/item/IM2_1982_18_1_a4/

[1] Agmon S., Nirenberg L., “Properties of solutions of ordinary differential equations in Banach space”, Comm. Pure Appl. Math., 16 (1963), 121–239 | DOI | MR | Zbl

[2] Kondratev V. A., “Kraevye zadachi dlya parabolicheskikh uravnenii v zamknutykh oblastyakh”, Tr. Mosk. matem. ob-va, 15, 1966, 400–451

[3] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. Mosk. matem. ob-va, 16, 1967, 219–292

[4] Pazy A., “Asymptotic expansions of solutions of ordinary differential equations in Hilbert space”, Arch. for Rat. Mech. Anal., 24:3 (1967), 193–218 | DOI | MR | Zbl

[5] Mazya V. G., Plamenevskii B. A., “Ob asimptoticheskom povedenii reshenii differentsialnykh uravnenii v gilbertovom prostranstve”, Izv. AN SSSR. Ser. matem., 36:5 (1972), 1080–1133 ; “Письмо в редакцию”, Изв. АН СССР. Сер. матем., 37:3 (1973), 709–710 | MR | Zbl

[6] Plamenevskii B. A., “Ob asimptoticheskom povedenii reshenii kvaziellipticheskikh uravnenii s operatornymi koeffitsientami”, Izv. AN SSSR. Ser. matem., 37 (1973), 1332–1375 | MR | Zbl

[7] Agmon S., Douglis A., Nirenberg L., “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions”, Comm. Pure Appl. Math., 17 (1964), 35–92 | DOI | MR | Zbl

[8] Yakubovich V. A., Starzhinskii B. M., Lineinye differentsialnye uravneniya s periodicheskimi koeffitsientami i ikh prilozheniya, Nauka, M., 1972 | MR

[9] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovykh prostranstvakh, Nauka, M., 1970 | MR

[10] Gelfand I. M., “Razlozhenie po sobstvennym funktsiyam uravneniya s periodicheskimi koeffitsientami”, Dokl. AN SSSR, 73 (1950), 1117–1120

[11] Lidskii V. B., “Razlozhenie po sobstvennym funktsiyam uravneniya s periodicheskimi koeffitsientami”, Prilozhenie k knige E. Ch. Titchmarsh, Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, t. 2, IL, M., 1961, 529–532

[12] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[13] Agranovich M. S., Vishik M. I., “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, Uspekhi matem. nauk, 19:3 (1964), 53–160

[14] Gokhberg I. I., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR

[15] Khermander L., Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, M., 1965 | MR