Geodesic
Necessary conditions for the solvability of one class of boundary value problems for quasielliptic systems
Matematičeskie trudy, Tome 21 (2018) no. 1, pp. 3-16 
L. N. Bondar'. Necessary conditions for the solvability of one class of boundary value problems for quasielliptic systems. Matematičeskie trudy, Tome 21 (2018) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/MT_2018_21_1_a0/
@article{MT_2018_21_1_a0,
     author = {L. N. Bondar'},
     title = {Necessary conditions for the solvability of one class of boundary value problems for quasielliptic systems},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--16},
     year = {2018},
     volume = {21},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2018_21_1_a0/}
}
TY  - JOUR
AU  - L. N. Bondar'
TI  - Necessary conditions for the solvability of one class of boundary value problems for quasielliptic systems
JO  - Matematičeskie trudy
PY  - 2018
SP  - 3
EP  - 16
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MT_2018_21_1_a0/
LA  - ru
ID  - MT_2018_21_1_a0
ER  - 
%0 Journal Article
%A L. N. Bondar'
%T Necessary conditions for the solvability of one class of boundary value problems for quasielliptic systems
%J Matematičeskie trudy
%D 2018
%P 3-16
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/MT_2018_21_1_a0/
%G ru
%F MT_2018_21_1_a0

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

We consider boundary value problems in a half-space for a class of quasielliptic systems with nonzero boundary functions.We assume that the boundary value problems satisfy the Lopatinskiĭ condition. Necessary conditions are given for their unique solvability in Sobolev spaces. In a particular case, these conditions coincide with sufficient conditions.

[1] Besov O. V., “Issledovanie odnogo semeistva funktsionalnykh prostranstv v svyazi s teoremami vlozheniya i prodolzheniya”, Tr. MIAN SSSR, 60, 1961, 42–81 | Zbl

[2] Bondar L. N., “Razreshimost kraevykh zadach dlya kvaziellipticheskikh sistem”, Vestn. Tamb. un-ta. Ser. Estestv. i tekhn. n., 16:3 (2011), 771–775

[3] Bondar L. N., “Usloviya razreshimosti kraevykh zadach dlya kvaziellipticheskikh sistem v poluprostranstve”, Differents. uravneniya, 48:3 (2012), 341–350 | Zbl

[4] Bondar L. N., Demidenko G. V., “Kraevye zadachi dlya kvaziellipticheskikh sistem”, Sib. matem. zhurn., 49:2 (2008), 256–273 | MR | Zbl

[5] Vekua I. N., Nekotorye obschie metody postroeniya razlichnykh variantov teorii obolochek, Nauka, M., 1982 | MR

[6] Volevich L. R., “Lokalnye svoistva reshenii kvaziellipticheskikh sistem”, Matem. sb., 59:3 (1962), 3–52 | MR | Zbl

[7] Demidenko G. V., “Integralnye operatory, opredelyaemye kvaziellipticheskimi uravneniyami. II”, Sib. matem. zhurn., 35:1 (1994), 41–65 | MR | Zbl

[8] Demidenko G. V., Uspenskii S. V., Uravneniya i sistemy, ne razreshennye otnositelno starshei proizvodnoi, Nauchnaya kniga, Novosibirsk, 1998 | MR

[9] Uspenskii S. V., Demidenko G. V., Perepelkin V. G., Teoremy vlozheniya i prilozheniya k differentsialnym uravneniyam, Nauchnaya kniga, Novosibirsk, 1984 | MR

[10] Yanushauskas A. I., Zadacha o naklonnoi proizvodnoi teorii potentsiala, Nauchnaya kniga, Novosibirsk, 1985 | MR

[11] Demidenko G. V., “On solvability of boundary value problems for quasi-elliptic systems in $\mathbb{R}^n_+$”, J. Anal. Appl., 4:1 (2006), 1–11 | DOI | MR | Zbl