Laplacian with Respect to a Measure on the Riemannian Manifold and the Dirichlet problem. I

摘要

We propose an L (2) -version of the Laplacian with respect to a measure on the infinite-dimensional Riemannian manifold. The Dirichlet problem for equations with the proposed Laplacian is solved in a region of the Riemannian manifold from a certain class.