Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of Ground States of Nonlocal-Interaction Energies   We investigate which nonlocal-interaction energies have a ground state
(global minimizer). We consider this question over the space of probability
measures and establish a sharp condition for the existence of ground states. We
show that this condition is closely related to the notion of stability (i.e.
$H$-stability) of pairwise interaction potentials. Our approach uses the direct
method of the calculus of variations.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph