Minimizing measures on condensers of infinitely many plates

Details Minimizing measures on condensers of infinitely many plates Minimizing measures on condensers of infinitely many plates

2010-01-25

arxiv.org/abs/1001.4369v1

Mathematics

Classical Analysis and ODEs

22 pages

Scientific paper

The study deals with a minimal energy problem over noncompact classes of infinite dimensional vector measures in a locally 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 are mutually disjoint, and the interaction matrix for the charges corresponds to an electrostatic interpretation of a condenser. For all positive definite kernels satisfying Fuglede's condition of consistency between the weak* and strong topologies, sufficient conditions for the existence of equilibrium measures are established and properties of their uniqueness, vague compactness, and continuity are studied.

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