Geodesic
Elliptic problems with nonlocal conditions near the boundary
Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 293-316 Cet article a éte moissonné depuis la source Math-Net.Ru

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An elliptic equation of order $2m$ with nonlocal conditions near the boundary is considered. The presence of nonlocal terms in the boundary conditions leads to the appearance of singularities in the solution. The Noether property is proved for this problem in weighted spaces and asymptotics of the solutions are obtained. These results are applied to the study of the solvability and smoothness of solutions of elliptic differential-difference equations. Bibliography: 22 titles. 
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A. L. Skubachevskii. Elliptic problems with nonlocal conditions near the boundary. Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 293-316. http://geodesic.mathdoc.fr/item/SM_1987_57_1_a18/

[1] Carleman T., “Sur la theorie des equations integrales et ses applications”, Verhandlungen des International Mathematiker–Kongresses, 1, Zürich, 1932, 138–151 | Zbl

[2] Browder F., “Non-local elliptic boundary value problems”, Amer. J. Math., 86:4 (1964), 735–750 | DOI | MR | Zbl

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

[4] Karlovich Yu. I., Kravchenko V. G., Litvinchuk G. S., “Teoriya Netera singulyarnykh integralnykh operatorov so sdvigom”, Izv. VUZov, Matem., 1983, no. 4, 3–27 | MR | Zbl

[5] Bitsadze A. V., Samarskii A. A., “O nekotorykh prosteishikh obobscheniyakh lineinykh ellipticheskikh kraevykh zadach”, DAN SSSR, 185:4 (1969), 739–740 | Zbl

[6] Bitsadze A. V., “K teorii nelokalnykh kraevykh zadach”, DAN SSSR, 277:1 (1984), 17–19 | MR | Zbl

[7] Gordeziani D. G., O metodakh resheniya odnogo klassa nelokalnykh kraevykh zadach, Izd-vo TGU, Tbilisi, 1981 | MR | Zbl

[8] Zhitarashu N. V., Eidelman S. D., “O nelokalnykh granichnykh zadachakh dlya ellipticheskikh uravnenii”, Matem. issledovaniya, Kishinev, 6:2(20) (1971), 63–73 | MR | Zbl

[9] Kamynin L. I., “Edinstvennost reshenii kraevykh zadach dlya vyrozhdayuschegosya ellipticheskogo uravneniya vtorogo poryadka”, Differents. uravneniya, 14:1 (1978), 39–49 | MR | Zbl

[10] Paneyakh V. P., “O nekotorykh nelokalnykh kraevykh zadachakh dlya lineinykh differentsialnykh operatorov”, Mat. zametki, 35:3 (1984), 425–434 | MR | Zbl

[11] Roitberg Ya. A., Sheftel Z. G., “Ob odnom klasse obschikh nelokalnykh ellipticheskikh zadach”, DAN SSSR, 192:3 (1970), 511–513 | MR | Zbl

[12] Skubachevskii A. L., “O spektre nekotorykh nelokalnykh ellipticheskikh kraevykh zadach”, Matem. sb., 117(159) (1982), 548–558. | MR

[13] Skubachevskii A. L., “Nelokalnye ellipticheskie zadachi s parametrom”, Matem. sb., 121(163) (1983), 201–210 | MR

[14] Samarskii A. A., “O nekotorykh problemakh teorii differentsialnykh uravnenii”, Differents. uravneniya, 16:11 (1980), 1925–1935 | MR | Zbl

[15] Sommerfeld A., “Ein Beitrag zur hydrodynamischen Erklärung der turbulenten Flussigkeitsbewegungen”, Atti del IV Congr. intern, dei Matem., III, Roma, 1909, 116–124

[16] Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh lineinykh differentsialnykh uravnenii, Petrograd, 1917 | Zbl

[17] Picone M., “Equazione integrale traducente il piu generale problema lineare”, Atti. Ace. dei Lincei, 15:6 (1932), 942–948 | Zbl

[18] Mikhailov V. P., “O bazisakh Rissa v $L_2(0,1)$”, DAN SSSR, 144:5 (1962), 981–984

[19] Agranovich M. S, Vishik M. I., “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, UMN, 19:3 (1964), 53–161 | Zbl

[20] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. MMO, 16 (1967), 209–292 | Zbl

[21] Kondratev V. A., “Kraevye zadachi dlya parabolicheskikh uravnenii v zamknutykh oblastyakh”, Tr. MMO, 15 (1966), 400–451 | Zbl

[22] Blekher I. M., “Ob operatorakh, zavisyaschikh meromorfno ot parametra”, Vestn. MGU., Ser. 1 matem., mekh., 1969, no. 5, 30–36 | Zbl