Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower semicontinuity for integral functionals in the space of functions
  of bounded deformation via rigidity and Young measures   We establish a general weak* lower semicontinuity result in the space
$\BD(\Omega)$ of functions of bounded deformation for functionals of the form
$$\Fcal(u) := \int_\Omega f \bigl(x, \Ecal u \bigr) \dd x + \int_\Omega
f^\infty \Bigl(x, \frac{\di E^s u}{\di \abs{E^s u}} \Bigr) \dd \abs{E^s u} +
\int_{\partial \Omega} f^\infty \bigl(x, u|_{\partial \Omega} \odot n_\Omega
\bigr) \dd \Hcal^{d-1}$$, $u \in \BD(\Omega)$. The main novelty is that we
allow for non-vanishing Cantor-parts in the symmetrized derivative $Eu$. The
proof is accomplished via Jensen-type inequalities for generalized Young
measures and a construction of good blow-ups, which is based on local rigidity
arguments for some differential inclusions involving symmetrized gradients.
This strategy allows us to establish the lower semicontinuity result without an
Alberti-type theorem in $\BD(\Omega)$, which is not available at present. We
also include existence and relaxation results for variational problems in
$\BD(\Omega)$, as well as a complete discussion of some differential inclusions
for the symmetrized gradient in two dimensions.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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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: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con