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

• Datum: 2008
• Hauptverfasser: Bernatskaya, J. N., Бернацька, Ю. Н.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2008
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3206
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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 potentia...