Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase-field approximation for a class of cohesive fracture energies with
  an activation threshold   We study the $\Gamma$-limit of Ambrosio-Tortorelli-type functionals
$D_\varepsilon(u,v)$, whose dependence on the symmetrised gradient $e(u)$ is
different in $\mathbb{A} u$ and in $e(u)-\mathbb{A} u$, for a
$\mathbb{C}$-elliptic symmetric operator $\mathbb{A}$, in terms of the
prefactor depending on the phase-field variable $v$. This is intermediate
between an approximation for the Griffith brittle fracture energy and the one
for a cohesive energy by Focardi and Iurlano. In particular we prove that
$G(S)BD$ functions with bounded $\mathbb{A}$-variation are $(S)BD$.

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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph