On lower order of mappings with finite length distortion

For mappings of finite distortion actively investigated last 15–20 years, problems of a so-called lower order are discussed. It is proved that, mappings with finite length distortion $f:D\to {\mathbb{R}}^n,$ $n\ge 2,$ which have locally integrable other dilatation in degree $\alpha >n-1,$ and have a finite asymptotic value are of a uniformly lower bounded lower order.