The solution of mixed boundary value problems with the reference ellipsoid as boundary

In this paper we study the following mixed boundary value problem where is the reference ellipsoid, and T the disturbing potential. With the help of the variational principles of partial differential equations and the expression of ellipsoidal harmonic series, we give a linear system related to the coefficients of the ellipsoidal harmonic series. Hence the solution of the problem can be obtained in the form of ellipsoidal harmonic series, which supplies us an important theoretical basis for making use of data given by satellite altimetry measurements more efficiently. Received: 16 January 1996; Accepted: 22 January 1997