Ukrainian Mathematical Journal

, Volume 60, Issue 7, pp 1028–1044 | Cite as

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.


Riemannian Manifold Parabolic Equation Fundamental Solution Sectional Curvature Jacobi Equation 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • J. N. Bernatskaya
    • 1
  1. 1.“Kyevo-Mohylyans’ka Akademiya” National UniversityKievUkraine

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