Knowledge Bank

The report reviews progress in the mathematical formulation and treatment of the geodetic boundary-value problem, in particular, the existence and uniqueness theorems of L. Hörmander and the gravity space approach due to F. Sanso. The method of Hörmander uses a very advanced inverse function theorem of nonlinear functional analysis. Sanso has transformed Molodensky's free boundary-value problem into a fixed boundary-value problem in "gravity space", thereby essentially reducing the mathematical complexity. As a linear approximation, the gravity space approach gives identical results to the conventional linearization, but gravity space appears superior for treating questions of existence and uniqueness of the solution, although it is restricted to the pure gravitational case without centrifugal force.