Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The asymptotically sharp Korn interpolation and second inequalities for
  shells   We consider shells in three dimensional Euclidean space which have bounded
principal curvatures. We prove Korn's interpolation (or the so called first and
a half\footnote{The inequality first introduced in [6]}) and second
inequalities on that kind of shells for $\Bu\in W^{1,2}$ vector fields,
imposing no boundary or normalization conditions on $\Bu.$ The constants in the
estimates are optimal in terms of the asymptotics in the shell thickness $h,$
having the scalings $h$ or $O(1).$ The Korn interpolation inequality reduces
the problem of deriving any linear Korn type estimate for shells to simply
proving a Poincar\'e type estimate with the symmetrized gradient on the right
hand side. In particular this applies to linear geometric rigidity estimates
for shells, i.e., Korn's fist inequality without boundary conditions.

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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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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: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph