Compactness和$GSBD$中的下半连续性
Compactness and lower semicontinuity in $GSBD$
摘要：
本文证明了$GSBD$中关于Griffith能量有界序列的一个紧性和连续性结果。这推广了Ambrosio的$(G)SBV$和Belgini-Coscia-Dal Maso的$SBD$中的经典结果.因此，静态问题的Francfort-Marigo的变分方法裂纹扩展承认（弱）的解决方案。此外，我们得到了一个紧性的最小适当的Ambrosio-Tortorelli的型能量，我们最近显示的$Γ$ -收敛到格里菲斯能量。
英文摘要：
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 $Γ$-convergence to Griffith energy.
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