The Spheroidal Stokes Boundary Value Problem (extended abstract)

The target of the spheroidal Gauss-Listing geoid determination is presented as a solution of the spheroidal fixed-free two-boundary value problem based on a spheroidal Bruns transformation (spheroidal Bruns formula). The nonlinear spheroidal Bruns transform (nonlinear spheroidal Bruns formula), and the spheroidal fixed part and the spheroidal free part of the two-boundary value problem have been derived. Four different spheroidal gravity models are treated, in particular whether they pass the test to fit to the postulate of a level ellipsoidal gravity field, namely of Somigliana-Pizzetti type. The free part of the fixed-free two-boundary value problem in its linearized version agrees with the spheroidal Stokes boundary value problem.