On the explicit determination of stability constants for linearized geodetic boundary value problems

The theory of GBVPs provide the basis to the approximate methods used to compute global gravity models. A standard approximation procedure is least squares, which implicitly assumes that data, e.g. gravity disturbance and gravity anomaly, are given functions in L2(S). We know that solutions in these cases exist, but uniqueness (and coerciveness which implies stability of the numerical solutions) is the real problem. Conditions of uniqueness for the linearized fixed boundary and Molodensky problems are studied in detail. They depend on the geometry of the boundary; however, the case of linearized fixed boundary BVP puts practically no constraint on the surface S, while the linearized Molodensky BVP requires the previous knowledge of very low harmonics, for instance up to degree 25, if we want the telluroid to be free to have inclinations up to 60°.