Compactness and lower semicontinuity in $GSBD$
Functional Analysis
2018-09-26 v2
Abstract
In this paper, we prove a compactness and semicontinuity result in for sequences with bounded Griffith energy. This generalises classical results in by Ambrosio and 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 -convergence to Griffith energy.
Cite
@article{arxiv.1802.03302,
title = {Compactness and lower semicontinuity in $GSBD$},
author = {Antonin Chambolle and Vito Crismale},
journal= {arXiv preprint arXiv:1802.03302},
year = {2018}
}
Comments
to appear in J. Eur. Math. Soc. (JEMS)