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A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in $W^{1,n}$. (arXiv:1707.03801v2 [math.AP] UPDATED)
来源于:arXiv
In this paper we prove a lower semicontinuity result of Reshetnyak type for a
class of functionals which appear in models for small-strain elasto-plasticity
coupled with damage. To do so we characterise the limit of measures
$\alpha_k\,\mathrm{E}u_k$ with respect to the weak convergence
$\alpha_k\rightharpoonup \alpha$ in $W^{1,n}(\Omega)$ and the weak$^*$
convergence $u_k\stackrel{*}\rightharpoonup u$ in $BD(\Omega)$, $\mathrm{E}$
denoting the symmetrised gradient. A concentration compactness argument shows
that the limit has the form $\alpha\,\mathrm{E}u+\eta$, with $\eta$ supported
on an at most countable set. 查看全文>>