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The study deals with a minimal energy problem in the presence of an externalfield over noncompact classes of vector measures of infinite dimension in alocally compact space. The components are positive measures (charges)satisfying certain normalizing assumptions and supported by given closed sets(plates) with the sign +1 or -1 prescribed such that oppositely signed sets aremutually disjoint, and the interaction matrix for the charges corresponds to anelectrostatic interpretation of a condenser. For all positive definite kernelssatisfying Fuglede's condition of consistency between the weak* and strongtopologies, sufficient conditions for the existence of equilibrium measures areestablished and properties of their uniqueness, vague compactness, andcontinuity are studied. We also obtain variational inequalities for theweighted equilibrium potentials, single out their characteristic properties,and analyze continuity of the equilibrium constants.

Equilibrium problems for infinite dimensional vector potentials with external fields