Boundary value problems for second-order elliptic and parabolic operators on infinite-dimensional manifolds with boundary

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.
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