Bessel Potential spaces

Question

Let $\Omega_1,\Omega_2 \subset \mathbb{R}$ be bounded. The mapping $F: \Omega_1 \rightarrow \Omega_2$ shall be bijective, continuously differentiable and such that $||DF(x)||$ and $||(DF(x))^{-1}||$ are bounded in a suitable matrix norm for all $x$. Show that $v \in H^{1,2}(\Omega_2)$ implies that $v \circ F \in H^{1,2}(\Omega_1)$