Stanislav Hencl and Jani Onninen
Abstract: Let $\Omega$ be a domain in $\mathbb R^n$, $n = 2,3$. Suppose that a sequence of Sobolev homeomorphisms $f_k\colon \Omega \to\mathbb R^n$ with positive Jacobian determinants, $J(x,f_k) > 0$, converges weakly in $W^{1,p}(\Omega,\mathbb R^n)$, for some $p > 1$, to a mapping $f$. We show that $J(x,f) > 0$ a.e. in \Omega$.
Preprint: KMA Preprint Series, MATH-KMA-2013/438