2017
Том 69
№ 9

All Issues

Equilibrium Problems for Potentials with External Fields

Zorii N. V.

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Abstract

We investigate the problem on the minimum of energy over fairly general (generally speaking, noncompact) classes of real-valued Radon measures associated with a system of sets in a locally compact space in the presence of external fields. The classes of admissible measures are determined by a certain normalization or by a normalization and a certain majorant measure σ. In both cases, we establish sufficient conditions for the existence of minimizing measures and prove that, under fairly general assumptions, these conditions are also necessary. We show that, for sufficiently large σ, there is a close correlation between the facts of unsolvability (or solvability) of both variational problems considered.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 10, pp 1588-1618.

Citation Example: Zorii N. V. Equilibrium Problems for Potentials with External Fields // Ukr. Mat. Zh. - 2003. - 55, № 10. - pp. 1315-1339.

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