On the lower order of mappings with finite length distortion

Abstract

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 → ℝn, n ≥ 2, whose outer dilatation is integrable to the power α > n − 1 with finite asymptotic limit have lower order bounded from below.