О поведении потенциала простого слоя для параболического уравнения на римановом многообразии

Анотація

A parabolic equation is considered on a Riemannian manifold of nonpositive section curvature (a Cartan–Hadamard-type manifold). The second boundary-value problem for this equation is set in a bounded domain whose surface is a smooth submanifold. It is proved that the gradient of the single-layer potential for such problem possesses a jump in crossing the submanifold similarly to its behavior in the Euclidean space.