Abstract
We prove that, similarly to the double-layer potential in \(\mathbb{R}^n \), the double-layer potential constructed in a Riemann manifold of nonpositive sectional curvature has a jump in passing through the surface where its density is defined.
This is a preview of subscription content, log in via an institution to check access.
Access this article
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Similar content being viewed by others
REFERENCES
E. M. Landis, Second-Order Equations of Elliptic and Parabolic Type [in Russian], Nauka, Moscow (1971).
H. P. McKean, Stochastic Integrals, Academic Press, New York (1969).
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964).
V. G. Bondarenko, “Parametrix method for a parabolic equation on a Riemannian manifold,” Ukr. Mat. Zh., 51, No. 11, 1443–1448 (1999).
V. G. Bondarenko, “Estimates of the heat kernel on a manifold of nonpositive curvature,” Ukr. Mat. Zh., 50, No. 8, 1129–1136 (1998).
I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Nauka, Moscow (1961).
Rights and permissions
About this article
Cite this article
Bernats'ka, J.M. Behavior of the Double-Layer Potential for a Parabolic Equation on a Manifold. Ukrainian Mathematical Journal 55, 712–728 (2003). https://doi.org/10.1023/B:UKMA.0000010251.45236.9b
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000010251.45236.9b