Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilibrium problems for infinite dimensional vector potentials with
  external fields   The study deals with a minimal energy problem in the presence of an external
field over noncompact classes of vector measures of infinite dimension 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. We also obtain variational inequalities for the
weighted equilibrium potentials, single out their characteristic properties,
and analyze continuity of the equilibrium constants.

7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc