SBV中拟凸体能的下半连续性与降维中的整表示
Lower semicontinuity of quasiconvex bulk energies in SBV and integral representation in dimension reduction
摘要：
利用Larsen关于某些有界变差函数序列的近似梯度结构的一个结果，给出了Ambrosio关于$SBV$中拟凸体能量的下半连续性定理的一个简短证明.它使一般化的$SBV$设置的分解引理的规模梯度的降维，也表明，从整体能量的角度来看，$SBV$降维问题可以减少到类似的索伯列夫空间框架。
英文摘要：
A result of Larsen concerning the structure of the approximate gradient of certain sequences of functions with Bounded Variation is used to present a short proof of Ambrosio's lower semicontinuity theorem for quasiconvex bulk energies in $SBV$. It enables to generalize to the $SBV$ setting the decomposition lemma for scaled gradients in dimension reduction and also to show that, from the point of view of bulk energies, $SBV$ dimensional reduction problems can be reduced to analogue ones in the Sobolev spaces framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
