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On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. “Kyevo-Mohylyans’ka Akademiya” National University, Kiev, Ukraine

    J. N. Bernatskaya

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  1. J. N. Bernatskaya
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 879–891, July, 2008.

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Bernatskaya, J.N. On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold. Ukr Math J 60, 1028–1044 (2008). https://doi.org/10.1007/s11253-008-0110-z

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  • DOI: https://doi.org/10.1007/s11253-008-0110-z

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