当前位置: X-MOL 学术J. Eur. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Compactness and lower semicontinuity in $GSBD$
Journal of the European Mathematical Society ( IF 2.5 ) Pub Date : 2020-11-12 , DOI: 10.4171/jems/1021
Antonin Chambolle 1 , Vito Crismale 1
Affiliation  

In this paper, we prove a compactness and semicontinuity result in $GSBD$ for sequences with bounded Griffith energy. This generalises classical results in $(G)SBV$ by Ambrosio and $SBD$ 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 $\Gamma$-convergence to Griffith energy.

中文翻译:

$GSBD$ 中的紧凑性和下半连续性

在本文中,我们证明了具有有限格里菲斯能量的序列在 $GSBD$ 中的紧凑性和半连续性结果。这概括了 Ambrosio 的 $(G)SBV$ 和 Bellettini-Coscia-Dal Maso 的 $SBD$ 中的经典结果。因此,Francfort-Marigo 的裂纹扩展变分方法中的静态问题承认(弱)解决方案。此外,我们获得了合适的 Ambrosio-Tortorelli 类型能量的最小化器的紧致性,为此我们最近展示了 $\Gamma$-收敛到格里菲斯能量。
更新日期:2020-11-12
down
wechat
bug