Publication at Faculty of Mathematics and Physics |
2005
Abstract
Let $f\in W^{1,n}(\Omega,\rn)$ be a continuous mapping so that the components of the preimage of each $y\in \rn$ are compact. We show that $f$ is open and discrete if $|Df(x)|^n\le K(x)J_f(x)$ a.e where $K(x)\ge 1$ and $K^{n-1}/\Phi(\log(e+K))\in L^1(\Omega)$ for a function $\Phi$ that satisfies $\int_1^{\infty}1/\Phi(t)dt=\infty$ and some technical conditions.