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Zeitschrift für Analysis und ihre Anwendungen


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Volume 8, Issue 6, 1989, pp. 501–514
DOI: 10.4171/ZAA/371

Published online: 1989-12-31

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

A.V. Levin and Vladimir G. Maz'ya[1]

(1) Linköping University, Sweden

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.

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Levin A.V., Maz'ya Vladimir: Asymptotics of the densities of harmonic potentials near the apex of a cone (in Russian). Z. Anal. Anwend. 8 (1989), 501-514. doi: 10.4171/ZAA/371