Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An elliptic regularity theorem for fractional partial differential
  operators   We present and prove a version of the elliptic regularity theorem for partial
differential equations involving fractional Riemann-Liouville derivatives. In
this case, regularity is defined in terms of Sobolev spaces $H^s(X)$: if the
forcing of a linear elliptic fractional PDE is in one Sobolev space, then the
solution is in the Sobolev space of increased order corresponding to the order
of the derivatives. We also mention a few applications and potential extensions
of this result.

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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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: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: econ