Geodesic
On conditions for extending the trace and imbedding for Banach spaces of infinitely differentiable functions
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 91-112 
G. S. Balashova. On conditions for extending the trace and imbedding for Banach spaces of infinitely differentiable functions. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 91-112. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a5/
@article{SM_1994_78_1_a5,
     author = {G. S. Balashova},
     title = {On conditions for extending the~trace and imbedding for {Banach} spaces of infinitely differentiable functions},
     journal = {Sbornik. Mathematics},
     pages = {91--112},
     year = {1994},
     volume = {78},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_1_a5/}
}
TY  - JOUR
AU  - G. S. Balashova
TI  - On conditions for extending the trace and imbedding for Banach spaces of infinitely differentiable functions
JO  - Sbornik. Mathematics
PY  - 1994
SP  - 91
EP  - 112
VL  - 78
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1994_78_1_a5/
LA  - en
ID  - SM_1994_78_1_a5
ER  - 
%0 Journal Article
%A G. S. Balashova
%T On conditions for extending the trace and imbedding for Banach spaces of infinitely differentiable functions
%J Sbornik. Mathematics
%D 1994
%P 91-112
%V 78
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1994_78_1_a5/
%G en
%F SM_1994_78_1_a5

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

This paper is a continuation of investigations begun in [1]–[3]. Conditions are obtained for the existence of a function in an infinite-order Sobolev space with specified values of the function itself and of all its derivatives on the boundary of the domain, and criteria are established for imbeddings and compact imbeddings of some of the indicated spaces.

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

[2] Balashova G. S., “O teoremakh vlozheniya prostranstv beskonechno differentsiruemykh funktsii”, Matem. zametki, 35:4 (1984), 505–516 | MR | Zbl

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

[4] Dubinskii Yu. A., “O netrivialnosti nekotorykh klassov funktsii i razreshimosti nelineinykh obyknovennykh differentsialnykh uravnenii beskonechnogo poryadka”, Differents. uravneniya, 10:2 (1974), 231–240 | MR | Zbl

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

[6] Balashova G. S., “Netrivialnost nekotorogo klassa funktsii i razreshimost nelineinykh differentsialnykh uravnenii beskonechnogo poryadka”, Trudy MEI., 1978, no. 357, 11–13 | MR

[7] Dubinskii Yu. A., “O sledakh funktsii iz prostranstv Soboleva beskonechnogo poryadka i neodnorodnoi zadache Koshi-Dirikhle”, Differents. uravneniya, 14:6 (1978), 1002–1012 | MR | Zbl

[8] Balashova G. S., “Teoremy vlozheniya banakhovykh prostranstv beskonechno differentsiruemykh funktsii”, Matem. sb., 128(170):1(9) (1985), 66–81 | MR