Ciarlet Nečas condition in fractional Sobolev spaces

Let $s\in (\frac{n}{n+1},1)$, $\mathrm{\Omega }\subset {\mathbb{R}}^n$ be an open set and let $f\in W^{s,n\mathrm{/}s}(\mathrm{\Omega },{\mathbb{R}}^n)$ be mapping with positive distributional Jacobian ${\mathcal{J}}_f>0$ which models some deformation in fractional Nonlinear Elasticity. We show change of variables formula in this class and as a consequence we show that the analogue of Ciarlet-Nečas condition ${\mathcal{J}}_f(\mathrm{\Omega })=\mathrm{\mid }f(\mathrm{\Omega })\mathrm{\mid }$ implies that our mapping is one-to-one a.e.