Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lojasiewicz--Simon gradient inequalities for the harmonic map energy
  function   We apply our abstract gradient inequalities developed by the authors in
arXiv:1510.03817 to prove Lojasiewicz--Simon gradient inequalities for the
harmonic map energy function using Sobolev spaces which impose minimal
regularity requirements on maps between closed, Riemannian manifolds. Our
Lojasiewicz--Simon gradient inequalities for the harmonic map energy function
generalize those of Kwon (2002), Liu and Yang (2010), Simon (1983, 1985), and
Topping (1997).

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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex