SOLUTION TO THE STOKES BOUNDARY-VALUE PROBLEM ON AN ELLIPSOID OF REVOLUTION

We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity to of the ellipsoid of revolution is less than 0-65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the O(e(0)(2))-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point Psi=0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function.