On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold
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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.
KeywordsRiemannian Manifold Parabolic Equation Fundamental Solution Sectional Curvature Jacobi Equation
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