Geodesic
On a coercive inequality for an elliptic operator in infinitely many independent variables
Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 395-406 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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