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arXiv 2011.031982020-11-06math.AP

Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A Note

Armin Schikorra, James M. Scott

英文摘要：

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.

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