On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold
On a Riemannian manifold of nonpositive sectional curvature (Cartan-Hadamard-type manifold), we consider a parabolic equation. The second boundary-value problem for this equation is set in a bounded domain whose surface is a smooth submanifold. We prove that the gradient of the simple-layer potential for this problem has a jump when passing across the submanifold, similarly to its behavior in a Euclidean space.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 7, pp 1028-1044.
Citation Example: Bernatskaya J. N. On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold // Ukr. Mat. Zh. - 2008. - 60, № 7. - pp. 879–891.