Abstract
One possible interpretation of the geodetic use of DC is the so-called Change of Boundary method. This is essentially an iterative procedure pulling back the data from the actual complicated boundary to a Bjerhammer sphere, solving the corresponding BVP by a Poisson kernel and then going to residuals. A rigorous proof of convergence of the above method is still lacking, although a fine perturbative analysis conducted in Appendix A seems to answer in positive sense to such question.
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References
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Sansò, F., Sideris, M.G. (2017). The Change of Boundary Approach. In: Geodetic Boundary Value Problem: the Equivalence between Molodensky’s and Helmert’s Solutions. SpringerBriefs in Earth Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-46358-2_6
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DOI: https://doi.org/10.1007/978-3-319-46358-2_6
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