Published Paper

Inserted: 13 jul 2017
Last Updated: 21 feb 2019

Journal: NoDEA Nonlinear Differential Equations Appl.
Volume: 25
Pages: Article 25:16
Year: 2018
Doi: 10.1007/s00030-018-0507-9

Abstract:

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.

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