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On a minimal element for a family of bodies producing the same external gravitational field. (English) Zbl 1115.86002
Summary: A minimal element, mother body, for a family of bodies producing the same external gravitational field is the body in the family, whose support has Lebesgue measure zero and satisfies some additional requirements. The finite algorithm of constructing mother bodies in \(\mathbb R^2\) is suggested. The local structure of mother bodies near singular points of continued logarithmic potential is investigated in generic positions.

MSC:
86A20 Potentials, prospecting
35A15 Variational methods applied to PDEs
86A22 Inverse problems in geophysics
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