Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower semicontinuity in $GSBD$ for nonautonomous surface integrals   We provide a sufficient condition for lower semicontinuity of nonautonomous
noncoercive surface energies defined on the space of $GSBD^p$ functions, whose
dependence on the $x$-variable is $W^{1,1}$ or even $BV$: the notion of
nonautonomous symmetric joint convexity, which extends the analogous definition
devised for autonomous integrands in \cite{FPS} where the conservativeness of
the approximating vector fields is assumed. This condition allows to extend to
our setting a nonautonomous chain formula in $SBV$ obtained in \cite{ACDD}, and
this is a key tool in the proof of the lower semicontinuity result. This new
joint convexity can be checked explicitly for some classes of surface energies
arising from variational models of fractures in inhomogeneous materials.

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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th