Bernatska J. Some problems for a parabolic equation on a Rieman-nian manifold

Existence of a double-layer potential gap for a self-adjoint parabolic equation on the manifold is proven. A solution of a Dirihlet problem for the equation is built by the potential method, and an estimate of the solution convergence is obtained. A fundamental solution for the parabolic equation with drift on the manifold is built by the perturbation method with different initial approxi-mations and different conditions on the drift field. It is obtained a representation of a logarithmic gradient for the fundamental solution to the parabolic equation with drift as a sum of two vector fields: known and bounded.