The Analysis of the Geodetic Boundary Value Problem: State and Perspectives
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The geodetic boundary value problem is mathematically a freeboundary, oblique derivative boundary value problem for the Laplace operator. The solution of the problem is the determination of the shape of the Earth and of its gravity field. The analysis of such a problem, specially for its non-linear formulation, is hard, so it started only in 1976 with a paper by L. Hörmander .
Since then the research has continued for both the non-linear and the linearized version, till recent years. In this article the author tries to give an overview on the subject, including a new result for the so-called Simple Molodensky Problem.
Keywords.Geodetic boundary value problem linearization scalar and vector variants Molodensky problem
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