A lower semicontinuity result for linearised elastoplasticity coupled with damage in $W^{1,\gamma}$, $\gamma>1$
Abstract
We prove the lower semicontinuity of functionals of the form \[ \int \limits_\Omega \! V(\alpha) \, \mathrm{d} \mathrm{E} u \, , \] with respect to the weak converge of $\alpha$ in $W^{1,\gamma}(\Omega)$, $\gamma > 1$, and the weak* convergence of $u$ in $BD(\Omega)$, where $\Omega \subset \mathbb{R}^n$. These functional arise in the variational modelling of linearised elastoplasticity coupled with damage and their lower semicontinuity is crucial in the proof of existence of quasistatic evolutions. This is the first result achieved for subcritical exponents $\gamma < n$.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 DOI:
 10.48550/arXiv.1909.09615
 arXiv:
 arXiv:1909.09615
 Bibcode:
 2019arXiv190909615C
 Keywords:

 Mathematics  Analysis of PDEs