Geodesic
Solvability of Nonlocal Elliptic Problems in Dihedral Angles
Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 178-197.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider nonlocal elliptic problems in dihedral and plane angles. Such problems arise in the study of nonlocal problems in bounded domains for the case in which the support of nonlocal terms intersects the boundary. We study the Fredholm and unique solvability of this problem in the corresponding weighted spaces. Results are obtained by means of a priori estimates of the solutions and of Green's formula for nonlocal elliptic problems. 
@article{MZM_2002_72_2_a2,
     author = {P. L. Gurevich},
     title = {Solvability of {Nonlocal} {Elliptic} {Problems} in {Dihedral} {Angles}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {178--197},
     publisher = {mathdoc},
     volume = {72},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a2/}
}
TY  - JOUR
AU  - P. L. Gurevich
TI  - Solvability of Nonlocal Elliptic Problems in Dihedral Angles
JO  - Matematičeskie zametki
PY  - 2002
SP  - 178
EP  - 197
VL  - 72
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a2/
LA  - ru
ID  - MZM_2002_72_2_a2
ER  - 
%0 Journal Article
%A P. L. Gurevich
%T Solvability of Nonlocal Elliptic Problems in Dihedral Angles
%J Matematičeskie zametki
%D 2002
%P 178-197
%V 72
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a2/
%G ru
%F MZM_2002_72_2_a2
P. L. Gurevich. Solvability of Nonlocal Elliptic Problems in Dihedral Angles. Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 178-197. http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a2/

[1] Bitsadze A. V., “Ob odnom klasse uslovno razreshimykh nelokalnykh kraevykh zadach dlya garmonicheskikh funktsii”, Dokl. AN SSSR, 280:3 (1985), 521–524 | MR | Zbl

[2] Skubachevskii A. L., “Ellipticheskie zadachi s nelokalnymi usloviyami vblizi granitsy”, Matem. sb., 129 (171):2 (1986), 279–302 | MR

[3] Skubachevskii A. L., “Modelnye nelokalnye zadachi dlya ellipticheskikh uravnenii v dvugrannykh uglakh”, Differents. uravneniya, 26:1 (1990), 120–131 | MR

[4] Skubachevskii A. L., “O metode srezayuschikh funktsii v teorii nelokalnykh zadach”, Differents. uravneniya, 27:1 (1991), 128–139 | MR

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

[6] Mazya V. G., Plamenevskii B. A., “$L_p$-otsenki reshenii ellipticheskikh kraevykh zadach v oblastyakh s rebrami”, Tr. MMO, 37, URSS, M., 1978, 49–93 | MR | Zbl

[7] Nazarov S. A., Plamenevskii B. A., Ellipticheskie zadachi v oblastyakh s kusochno gladkoi granitsei, Nauka, M., 1991

[8] Roitberg Ya. A., Sheftel Z. G., “Formula Grina i teoremy o gomeomorfizmakh dlya nelokalnykh ellipticheskikh zadach”, Dokl. AN SSSR, 201:5 (1971), 1059–1062 | MR

[9] Ilin V. A., Moiseev E. I., “Apriornaya otsenka resheniya zadachi, sopryazhennoi k nelokalnoi kraevoi zadache pervogo roda”, Differents. uravneniya, 24:5 (1988), 795–804 | MR

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

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

[12] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973

[13] Krein S. G., Lineinye uravneniya v banakhovom prostranstve, Nauka, M., 1971

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

[15] Sheftel Z. G., “Energeticheskie neravenstva i obschie granichnye zadachi dlya ellipticheskikh uravnenii s razryvnymi koeffitsientami”, Sib. matem. zh., 6:3 (1965), 636–668 | MR | Zbl