Abstract
The Newton potential of the earth as well as its anomalous gravity potential are harmonic functions outside the earth body B, therefore the interest of geodesy in spaces of harmonic functions is quite justified. More precisely, from the mathematical point of view we are interested in a situation in which B is an open, simply connected bounded set, with a relatively smooth boundary S and \({\overline{B}}^{c}\,=\,\Omega \) (the complement of the closure of B) is simply connected too. Let us note explicitly that this prevents B from having holes in it or even single points removed.
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Sansò, F., Sideris, M.G. (2013). On Potential Theory and HS of Harmonic Functions. In: Sansò, F., Sideris, M. (eds) Geoid Determination. Lecture Notes in Earth System Sciences, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74700-0_13
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DOI: https://doi.org/10.1007/978-3-540-74700-0_13
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