Geodesic
Boundary value problems for second-order elliptic and parabolic operators on infinite-dimensional manifolds with boundary
Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 325-364 
M. I. Vishik; A. V. Marchenko. Boundary value problems for second-order elliptic and parabolic operators on infinite-dimensional manifolds with boundary. Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 325-364. http://geodesic.mathdoc.fr/item/SM_1973_19_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For elliptic operators with infinitely many variables, having a large parameter for the zero-order term, it is proved that the Dirichlet problem has a unique solution on $CL$-manifolds with boundary. The Green kernel of the associated invertible operator is a measure which depends on the point of observation as well as on the parameter. The existence of a unique solution of the first boundary value problem for a second-order parabolic operator with infinitely many variables on the direct product of a $CL$-manifold with boundary and the semi-axis $t\geqslant0$ is proved. Bibliography: 7 titles.

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

[2] P. M. Blekher, M. I. Vishik, “Ob odnom klasse psevdodifferentsialnykh operatorov s beskonechnym chislom peremennykh i ikh prilozheniyakh”, Matem. sb., 86 (128) (1971), 447–494

[3] M. I. Vishik, G. I. Eskin, “Uravneniya v svertkakh v ogranichennoi oblasti”, Uspekhi matem. nauk, XX:3 (123) (1965), 89–152

[4] I. M. Gelfand, N. Ya. Vilenkin, Nekotorye primeneniya garmonicheskogo analiza. Osnaschennye gilbertovy prostranstva, Fizmatgiz, Moskva, 1961

[5] M. I. Vishik, G. I. Eskin, “Parabolicheskie uravneniya v svertkakh v ogranichennoi oblasti”, Matem. sb., 71 (113) (1966), 162–170

[6] Yu. L. Daletskii, Ya. I. Shnaiderman, “Diffuziya i kvaziinvariantnye mery na beskonechnomernykh gruppakh Li”, Funkts. analiz, 3:2 (1969), 89–90

[7] J. Fells K. D. Elworthy, “Wiener integration on certain-manifolds”, Centro Internazionale Matematico Estivo (Corso tenuto a Varenna dal 20 al 29 Agosto), 1970, 69–94