2017
Том 69
№ 6

All Issues

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

Zorii N. V.

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Abstract

We investigate the well-known Gauss variational problem considered 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 potentials of vague and (or) strong limit points of minimizing sequences of measures. The results obtained are also specified for the Newton kernel in $\mathbb{R}^n$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 1, pp 70-99.

Citation Example: Zorii N. V. Necessary and Sufficient Conditions for the Solvability of the Gauss Variational Problem // Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 60–83.

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