Boundary integral equations of the method of potentials for the Laplace differential equation in a domain containing a conic point are considered. For the density of a double-layer (single-layer) potential in the case of Dirichlet’s (Neumann’s) problem, the asymptotic expansion in a neighbourhood of the conic point is derived and the corresponding coefficients are calculated. In the case of a circular cone, the summands of the asymptotic expansion and the dependence of the power exponent of its principal term on the apex angle of the cone are given.
Cite this article
A.V. Levin, Vladimir G. Maz'ya, Asymptotics of the densities of harmonic potentials near the apex of a cone (in Russian). Z. Anal. Anwend. 8 (1989), no. 6, pp. 501–514DOI 10.4171/ZAA/371