Abstract
In physical geodesy one considers several (exterior) Robin boundary value problems for the Laplace equation in three dimensions. The ellipsoidal Stokes problem, which occurs in context of gravimetric determination of the geoid, belongs to this class. Up to now, this and related problems have been treated with high order series expansions of spherical and spheroidal harmonics. In this article we investigate the nullfield method for this class of boundary value problems. An integral equation formulation is achieved, and existence and uniqueness conditions are attained in view of the Fredholm alternative. For the case that the underlying surface is a triaxial ellipsoid or an oblate spheroid, explicit expressions for the eigenvalues and eigenfunctions for the boundary integral operator are provided.
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