Weak limits of fractional Sobolev homeomorphisms are almost injective

Abstract

Let $\Omega \subset \mathbb {R}^n$ be an open set and $f_k \in W^{s,p}(\Omega ;\mathbb {R}^n)$ be a sequence of homeomorphisms weakly converging to $f \in W^{s,p}(\Omega ;\mathbb {R}^n)$. It is known that if $s=1$ and $p \gt n-1$ then $f$ is injective alm