Asymptotics of the densities of harmonic potentials near the apex of a cone (in Russian)

Abstract

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.