论文标题
分数Sobolev同构的限制较弱，几乎是注入性的：
Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A Note
论文作者
论文摘要
令$ω\ subset \ mathbb {r}^n $为打开集，而$ f_k \ in w^{s，p}（ω; \ \ m mathbb {r}^n）$是同构的顺序，是一系列同型薄弱的序列，在w^^{s，p}（s，p}; p}; \ mathbb^n $ f \ in w^^{s，p}中;众所周知，如果$ s = 1 $和$ p> n-1 $，那么$ f $几乎在域和目标中几乎无处不在。在本说明中，我们将这些结果扩展到（0,1）$和$ sp> n-1 $的情况。这特别适用于$ c^s $-Hölder地图。
Let $Ω\subset \mathbb{R}^n$ be an open set and $f_k \in W^{s,p}(Ω;\mathbb{R}^n)$ be a sequence of homeomorphisms weakly converging to $f \in W^{s,p}(Ω;\mathbb{R}^n)$. It is known that if $s=1$ and $p > n-1$ then $f$ is injective almost everywhere in the domain and the target. In this note we extend such results to the case $s\in(0,1)$ and $sp > n-1$. This in particular applies to $C^s$-Hölder maps.
