Geodesic
On the Dirichlet problem for an elliptic operator in a cylindrical domain of Hilbert space
Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 423-438 
N. N. Frolov. On the Dirichlet problem for an elliptic operator in a cylindrical domain of Hilbert space. Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 423-438. http://geodesic.mathdoc.fr/item/SM_1973_21_3_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A special class of elliptic operators with an infinite number of independent variables is introduced in the paper. The Dirichlet problem is considered in a cylindrical domain of Hilbert space for an operator belonging to this class. The investigation is based on the construction of a functional integral of double layer potential type. Bibliography: 11 titles.

[1] Yu. L. Daletskii, “Beskonechnomernye elllipticheskie operatory i svyazannye s nimi parabolicheskie uravneniya”, Uspekhi matem. nauk, XXII:4 (136) (1971), 3–54

[2] M. Ann. Piech, “A fundamental solution of the Parabolic equation on HiLbert space”, J. funct. analysis, 3:1 (1969), 85–114 | DOI | MR

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

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

[6] N. N. Frolov, “Teoremy vlozheniya dlya funktsii schetnogo chisla peremennykh i ikh prilozheniya k zadache Dirikhle”, DAN SSSR, 203:1 (1972), 39–42 | Zbl

[7] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, izd-vo «Nauka», Moskva, 1967

[8] S. D. Eidelman, Parabolicheskie sistemy, izd-vo «Nauka», Moskva, 1964 | MR

[9] S. G. Mikhlin, Kurs matematicheskoi fiziki, izd-vo «Nauka», Moskva, 1968 | MR

[10] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, izd-vo «Nauka», Moskva, 1964 | MR

[11] M. I. Vishik, A. V. Marchenko, “Kraevye zadachi dlya ellipticheskikh i parabolicheskikh operatorov vtorogo poryadka na beskonechnomernykh mnogoobraziyakh s kraem”, Matem. sb., 90 (132) (1973), 331–337