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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
Article
  • 26 Downloads

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.

Keywords

Riemannian Manifold Parabolic Equation Fundamental Solution Sectional Curvature Jacobi Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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