Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution |
| |
Authors: | Z Martinec E W Grafarend |
| |
Institution: | (1) Department of Geophysics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic e-mail: zdenek@hervam.troja.mff.cuni.cz , XX;(2) Department of Geodetic Science, Stuttgart University, Keplerstr. 11, D-70174 Stuttgart, Germany, DE |
| |
Abstract: | Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid
of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity
of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary
functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have
shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same
degree as that of the original spherical Poisson kernel.
Received: 4 June 1996 / Accepted: 7 April 1997 |
| |
Keywords: | , Green's function,Dirichlet boundary-value problem,Ellipsoid of revolution,ellipsoidal harmonics |
本文献已被 SpringerLink 等数据库收录! |
|