Abstract.
The problem of non-uniqueness of the scalar geodetic boundary value problem has been treated in recent geodetic literature. It has been pointed out that it is partly an open problem. It is demonstrated that in its nonlinear form, the problem exhibits many more features of ill-posedness than were known previously. Moreover, it is shown that the non-uniqueness appears mainly in the purely gravitational version of the problem, which is usually considered for mathematical analysis. It is also shown that in a more general version of the problem, which does not assume the rotational potential of the Earth to be known at the boundary, there is at least one special case of non-uniqueness, belonging approximately to a spheroidal planet of 1/116 flattening.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 2 October 2000 / Accepted: 12 June 2001
Rights and permissions
About this article
Cite this article
Lehmann, R. A new type of non-uniqueness for the scalar geodetic boundary value problem. Journal of Geodesy 75, 527–532 (2001). https://doi.org/10.1007/s001900100207
Issue Date:
DOI: https://doi.org/10.1007/s001900100207