Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Volume constrained minimizers of the fractional perimeter with a
  potential energy   We consider volume-constrained minimizers of the fractional perimeter with
the addition of a potential energy in the form of a volume inte- gral. Such
minimizers are solutions of the prescribed fractional curvature problem. We
prove existence and regularity of minimizers under suitable assumptions on the
potential energy, which cover the periodic case. In the small volume regime we
show that minimizers are close to balls, with a quantitative estimate.

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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph