Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compactness and lower semicontinuity in $GSBD$   In this paper, we prove a compactness and semicontinuity result in $GSBD$ for
sequences with bounded Griffith energy. This generalises classical results in
$(G)SBV$ by Ambrosio and $SBD$ by Bellettini-Coscia-Dal Maso. As a result, the
static problem in Francfort-Marigo's variational approach to crack growth
admits (weak) solutions. Moreover, we obtain a compactness property for
minimisers of suitable Ambrosio-Tortorelli's type energies, for which we have
recently shown the $\Gamma$-convergence to Griffith energy.

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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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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: funct-an
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The categories of this paper are: hep-th