On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold

  • J. N. Bernatskaya


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.
How to Cite
Bernatskaya, J. N. “On the Behavior of a Simple-Layer Potential for a Parabolic Equation on a Riemannian Manifold”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 7, July 2008, pp. 879–891, https://umj.imath.kiev.ua/index.php/umj/article/view/3206.
Research articles