TY - JOUR
AU - J. N. Bernatskaya
PY - 2008/07/25
Y2 - 2023/03/31
TI - On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 60
IS - 7
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3206
AB - 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.
ER -