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Necessary and Sufficient Conditions for the Solvability of the Gauss Variational Problem

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Abstract

We investigate the well-known Gauss variational problem over classes of Radon measures associated with a system of sets in a locally compact space. Under fairly general assumptions, we obtain necessary and sufficient conditions for its solvability. As an auxiliary result, we describe the potentials of vague and (or) strong limit points of minimizing sequences of measures. The results obtained are also specified for the Newton kernel in ℝn.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 60–83, January, 2005.

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Zorii, N.V. Necessary and Sufficient Conditions for the Solvability of the Gauss Variational Problem. Ukr Math J 57, 70–99 (2005). https://doi.org/10.1007/s11253-005-0172-0

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  • DOI: https://doi.org/10.1007/s11253-005-0172-0

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