Geodesic
Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations
Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 627-644 
Yu. A. Dubinskii. Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations. Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 627-644. http://geodesic.mathdoc.fr/item/SM_1978_34_5_a3/
@article{SM_1978_34_5_a3,
     author = {Yu. A. Dubinskii},
     title = {Traces of functions from {Sobolev} spaces of infinite order and inhomogeneous problems for nonlinear equations},
     journal = {Sbornik. Mathematics},
     pages = {627--644},
     year = {1978},
     volume = {34},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_5_a3/}
}
TY  - JOUR
AU  - Yu. A. Dubinskii
TI  - Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations
JO  - Sbornik. Mathematics
PY  - 1978
SP  - 627
EP  - 644
VL  - 34
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_1978_34_5_a3/
LA  - en
ID  - SM_1978_34_5_a3
ER  - 
%0 Journal Article
%A Yu. A. Dubinskii
%T Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations
%J Sbornik. Mathematics
%D 1978
%P 627-644
%V 34
%N 5
%U http://geodesic.mathdoc.fr/item/SM_1978_34_5_a3/
%G en
%F SM_1978_34_5_a3

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

The paper is devoted to the theory of “traces” in the spaces $$ W^\infty\{a_\alpha,p_\alpha\}(G)=\biggl\{u(x)\in C^\infty(G):\quad\sum_{|\alpha|=0}^{\infty}a_\alpha\|D^\alpha u\|_{p_\alpha}^{p_\alpha}<\infty\biggr\} $$ and to the inhomogeneous Dirichlet problem for elliptic equations of infinite order. A trace criterion is established, simple sufficient trace conditions are adduced, and the correctness of the indicated Dirichlet problem is proved on the basis of the results obtained. Bibliography: 6 titles.

[1] Yu. A. Dubinskii, “Prostranstva Soboleva beskonechnogo poryadka i povedenie reshenii nekotorykh kraevykh zadach pri neogranichennom vozrastanii poryadka uravneniya”, Matem. sb., 98(140) (1975), 163–184 | MR | Zbl

[2] Yu. A. Dubinskii, “Netrivialnost prostranstv Soboleva beskonechnogo poryadka v sluchae polnogo evklidova prostranstva i tora”, Matem. sb., 100(142) (1976), 436–446 | MR | Zbl

[3] S. Mandelbroit, Primykayuschie ryady. Regulyarizatsiya posledovatelnostei. Primeneniya, Gostekhizdat, Moskva, 1955

[4] I. Stein, G. Veiss, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, izd-vo “Mir”, Moskva, 1974 | MR

[5] A. Zigmund, Trigonometricheskie ryady, t. 1, 2, izd-vo “Mir”, Moskva, 1965 | MR

[6] Yu. A. Dubinskii, “Nelineinye ellipticheskie i parabolicheskie uravneniya”, Itogi nauki i tekhniki. Seriya “Sovremennye problemy matematiki”, 9, VINITI, Moskva, 1976, 5–130