Geodesic
Green function properties and generalized solutions of elliptic boundary value problems
Izvestiya. Mathematics , Tome 3 (1969) no. 1, pp. 105-130.

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We consider the properties of the Green functions of general boundary value problems for elliptic equations and the properties following from them of the adjoints of the resolvents. The results obtained are used to study generalized solutions. We prove existence and estimate theorems for generalized solutions in spaces that are the negatives of Höder spaces. 
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Yu. P. Krasovskii. Green function properties and generalized solutions of elliptic boundary value problems. Izvestiya. Mathematics , Tome 3 (1969) no. 1, pp. 105-130. http://geodesic.mathdoc.fr/item/IM2_1969_3_1_a7/

[1] Eidus D. M., “Otsenki proizvodnykh funktsii Grina”, Dokl. AN SSSR, 106 (1956), 207–209 | MR | Zbl

[2] Smolitskii X. L., “Otsenki proizvodnykh funktsii Neimana”, Dokl. AN SSSR, 106 (1956), 796–797

[3] Eidus D. M., “Neravenstva dlya funktsii Grina”, Matem. sb., 45(87) (1958), 455–470 | MR | Zbl

[4] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, M., 1957

[5] Agmon S., Duglis A., Nirenberg D., Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, M., 1962

[6] Berezanskii Yu. M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR

[7] Berezanskii Yu. M., Roitberg Ya. A., “Teorema o gomeomorfizmakh i funktsiya Grina dlya obschikh ellipticheskikh granichnykh zadach”, Ukr. matem. zhurn., XIX (1967), 3–31

[8] Madzhenes E., “Interpolyatsionnye prostranstva i uravneniya v chastnykh proizvodnykh”, Uspekhi matem. nauk, 21:2 (1966), 169–217 | MR

[9] Krasovskii Yu. P., “Issledovanie potentsialov, svyazannykh s kraevymi zadachami dlya ellipticheskikh uravnenii”, Izv. AN SSSR. Cer. matem., 31 (1967), 587–640 | MR | Zbl

[10] Krasovskii Yu. P., “Vydelenie osobennosti u funktsii Grina”, Izv. AN SSSR. Ser. matem., 31 (1967), 977–1010 | MR | Zbl

[11] Moren K., Metody gilbertova prostranstva, Mir, M., 1965 | MR

[12] Ivasishen S. D., Eidelman S. D., “Otsenki matritsy Grina odnorodnoi parabolicheskoi granichnoi zadachi”, Dokl. AN SSSR, 172 (1967), 1262–1265 | Zbl

[13] Eidelman S. D., Parabolicheskie sistemy, Nauka, M., 1964 | MR

[14] Ilin V. A., Shishmarev I. A., “Ob ekvivalentnosti sistem obobschennykh i klassicheskikh sobstvennykh funktsii”, Izv. AN SSSR. Ser. matem., 24 (1960), 757–774

[15] Ilin V. A., Shishmarev I. A., “Zadacha na sobstvennye funktsii dlya operatopa $Lu=\operatorname{div} [p(x) \operatorname{grad} u]-g(x)u$ s razryvnymi koeffitsientami”, Sib. mat. zh., II (1961), 520–536