On the lower order of mappings with finite length distortion

We study the problem of the so-called lower order for one kind of mappings with finite distortion, actively investigated in the recent 15–20 years. We prove that mappings with finite length distortion $f:D\rightarrow \mathbb{R}^n$, $n\ge 2$, whose outer dilatation is integrable to the power $\alpha>n-1$ with finite asymptotic limit have lower order bounded from below.