论文标题
Hausdorff的关键设置的luzin $ n $条件量度
Hausdorff measure of critical set for Luzin $N$ condition
论文作者
论文摘要
众所周知，W^{1，p}中的Sobolev同态$ f \ in w^{1，[ - 1,1]^n，[ - 1,1]^n）$均为任何$ p <n $映射$ c $ c $ c $ c $ c $ sero lebesgue $ n $ n $ dimensional量度，以映射到积极的积极度量上。我们研究了此关键集合$ c $的大小，并从由一般仪表函数定义的Hausdorff度量的角度来表征其下限和上限。
It is well-known that there is a Sobolev homeomorphism $f\in W^{1,p}([-1,1]^n,[-1,1]^n)$ for any $p<n$ which maps a set $C$ of zero Lebesgue $n$-dimensional measure onto the set of positive measure. We study the size of this critical set $C$ and characterize its lower and upper bounds from the perspective of Hausdorff measures defined by a general gauge function.
