论文标题
普遍的Lipschitz数字，良好的可怜性和准信息映射
Generalized Lipschitz numbers, fine differentiability, and quasiconformal mappings
论文作者
论文摘要
我们介绍了本地Lipschitz数字$ \ textrm {lip} \，u $的广义版本，并证明它可用于表征sobolev函数$ u \ in w _ {\ textrm {loc}}}}}^{1，p}（\ mathb r^n）$ 1 \ le p p \ per p \ pers funciption事实证明，这个概念在学习和建立新的联系之间是富有成效的，包括良好的可区分性，拉德马赫定理，费德勒对有限周边的集合的表征，最大功能的规律性，准构象映射的规律性，艾伯蒂的级别级别的理论以及一般的一般衡量标准。
We introduce a generalized version of the local Lipschitz number $\textrm{lip}\,u$, and show that it can be used to characterize Sobolev functions $u\in W_{\textrm{loc}}^{1,p}(\mathbb R^n)$, $1\le p\le \infty$, as well as functions of bounded variation. This concept turns out to be fruitful for studying, and for establishing new connections between, a wide range of topics including fine differentiability, Rademacher's theorem, Federer's characterization of sets of finite perimeter, regularity of maximal functions, quasiconformal mappings, Alberti's rank one theorem, as well as generalizations to metric measure spaces.
