Geodesic
Trace continuation in infinite-order Sobolev space on a multidimensional strip region
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 820-830 
G. S. Balashova. Trace continuation in infinite-order Sobolev space on a multidimensional strip region. Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 820-830. http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a2/
@article{MZM_1997_62_6_a2,
     author = {G. S. Balashova},
     title = {Trace continuation in infinite-order {Sobolev} space on a multidimensional strip region},
     journal = {Matemati\v{c}eskie zametki},
     pages = {820--830},
     year = {1997},
     volume = {62},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a2/}
}
TY  - JOUR
AU  - G. S. Balashova
TI  - Trace continuation in infinite-order Sobolev space on a multidimensional strip region
JO  - Matematičeskie zametki
PY  - 1997
SP  - 820
EP  - 830
VL  - 62
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a2/
LA  - ru
ID  - MZM_1997_62_6_a2
ER  - 
%0 Journal Article
%A G. S. Balashova
%T Trace continuation in infinite-order Sobolev space on a multidimensional strip region
%J Matematičeskie zametki
%D 1997
%P 820-830
%V 62
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a2/
%G ru
%F MZM_1997_62_6_a2

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

In the Sobolev infinite-order space on a multidimensional strip region we obtain conditions for the existence of a function that, together with all its derivatives, assumes prescribed values on the boundary. An example shows that the sufficient conditions for the trace continuation obtained in the present paper have a significant advantage over those obtained earlier. Furthermore, for spaces of some special type our conditions for trace continuation are both sufficient and necessary.

[1] Balashova G. S., “Nekotorye teoremy prodolzheniya v prostranstve Soboleva beskonechnogo poryadka i neodnorodnye kraevye zadachi”, Dokl. AN SSSR, 244:6 (1979), 1294–1297 | MR | Zbl

[2] Balashova G. S., “O teoremakh prodolzheniya v prostranstvakh beskonechno differentsiruemykh funktsii”, Matem. sb., 118 (160):3 (1982), 371–385 | MR

[3] Balashova G. S., “O prodolzhenii beskonechno differentsiruemykh funktsii”, Izv. AN SSSR. Ser. matem., 51:6 (1987), 1292–1308 | Zbl

[4] Balashova G. S., “Ob usloviyakh prodolzheniya sleda i vlozheniya dlya banakhovykh prostranstv beskonechno differentsiruemykh funktsii”, Matem. sb., 184:1 (1993), 105–128 | MR | Zbl

[5] Balashova G. S., “Teoremy prodolzheniya i vlozheniya dlya prostranstv Soboleva beskonechnogo poryadka”, Dokl. AN SSSR, 319:2 (1991), 267–270 | Zbl

[6] Dubinskii Yu. A., “Sledy funktsii iz prostranstv Soboleva beskonechnogo poryadka i neodnorodnye zadachi dlya nelineinykh uravnenii”, Matem. sb., 106 (148):1 (1978), 66–84 | MR | Zbl

[7] Mandelbroit S., Primykayuschie ryady. Regulyarizatsiya posledovatelnostei. Primeneniya, IL, M., 1955