Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sharp $L^p$ Korn interpolation and second inequalities in thin
  domains   In the present paper we extend the $L^2$ Korn interpolation and second
inequalities in thin domains, proven in [\ref{bib:Harutyunyan.4}], to the space
$L^p$ for any $1<p<\infty.$ A thin domain in space is roughly speaking a shell
with non-constant thickness around a smooth enough two dimensional surface. The
inequality that we prove in $L^p$ holds for practically any thin domain
$\Omega\subset\mathbb R^3$ and any vector field $\Bu\in W^{1,p}(\Omega).$ The
constants in the estimate are asymptotically optimal in terms of the domain
thickness $h.$ This in particular solves the problem of finding the asymptotics
of the optimal constant in the classical Korn second inequality in $L^p$ for
thin domains in terms of the domain thickness in almost full generality. The
remarkable fact is that the interpolation inequality reduces the problem of
estimating the gradient $\nabla\Bu$ in terms of the strain $e(\Bu)$ to the
easier problem of estimating only the vector field $\Bu$, which is a
Korn-Poincar\'e inequality.

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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph