Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fractional Korn-type inequality   We show that a class of spaces of vector fields whose semi-norms involve the
magnitude of "directional" difference quotients is in fact equivalent to the
class of fractional Sobolev spaces. The equivalence can be considered a
Korn-type characterization of fractional Sobolev spaces. We use the result to
understand better the energy space associated to a strongly coupled system of
nonlocal equations related to a nonlocal continuum model via peridynamics.
Moreover, the equivalence permits us to apply classical space embeddings in
proving that weak solutions to the nonlocal system enjoy both improved
differentiability and improved integrability.

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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: q-alg