Geodesic
On a coercive inequality for an elliptic operator in infinitely many independent variables
Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 395-406 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present paper a coercive inequality is established for an infinite-dimensional elliptic differential operator of order $2m$, and a theorem on smoothness of a generalized solution of the Dirichlet problem for an equation containing such an operator is established. Bibliography: 7 titles. 
@article{SM_1973_19_3_a2,
     author = {N. N. Frolov},
     title = {On~a~coercive inequality for an elliptic operator in infinitely many independent variables},
     journal = {Sbornik. Mathematics},
     pages = {395--406},
     year = {1973},
     volume = {19},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_3_a2/}
}
TY  - JOUR
AU  - N. N. Frolov
TI  - On a coercive inequality for an elliptic operator in infinitely many independent variables
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 395
EP  - 406
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1973_19_3_a2/
LA  - en
ID  - SM_1973_19_3_a2
ER  - 
%0 Journal Article
%A N. N. Frolov
%T On a coercive inequality for an elliptic operator in infinitely many independent variables
%J Sbornik. Mathematics
%D 1973
%P 395-406
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1973_19_3_a2/
%G en
%F SM_1973_19_3_a2
N. N. Frolov. On a coercive inequality for an elliptic operator in infinitely many independent variables. Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 395-406. http://geodesic.mathdoc.fr/item/SM_1973_19_3_a2/

[1] Yu. L. Daletskii, “Beskonechnomernye ellipticheskie operatory i svyazannye s nimi parabolicheskie uravneniya”, Uspekhi matem. nauk, XXII:4 (136) (1967), 3–54

[2] M. I. Vishik, “Parametriks ellipticheskikh operatorov s beskonechnym chislom nezavisimykh peremennykh”, Uspekhi matem. nauk, XXVI:2 (158) (1971), 155–174

[3] P. M. Blekher, M. I. Vishik, “Ob odnom klasse psevdodifferentsialnykh operatorov s beskonechnym chislom peremennykh i ikh prilozheniyakh”, Matem. sb., 86 (128) (1971), 446–494 | Zbl

[4] N. N. Frolov, O zadache Dirikhle dlya ellipticheskikh differentsialnykh uravnenii s beskonechnomernymi operatorami, dissertatsiya, Voronezh, 1970

[5] L. Gross, “Potential theory on Hilbert space”, J. funct. analysis, 1 (1967), 123–181 | DOI | MR | Zbl

[6] N. N. Frolov, “Teoremy vlozheniya dlya prostranstv funktsii schetnogo chisla peremennykh, I”, Trudy in-ta matematiki VGU, 1970, no. 1, 205–218

[7] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, izd-vo «Naukova dumka», Kiev, 1965 | MR