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

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. 
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     author = {M. I. Vishik and A. V. Marchenko},
     title = {Boundary value problems for second-order elliptic and parabolic operators on infinite-dimensional manifolds with boundary},
     journal = {Sbornik. Mathematics},
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     volume = {19},
     number = {3},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_3_a0/}
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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/