Radial Limits of Mappings of Bounded and Finite Distortion

Abstract

We give sufficient conditions for mappings defined on the unit ball of ℝn to have radial limits almost everywhere. In particular, we show that if f:B(0,1)→ℝn is a mapping with exponentially integrable distortion satisfying the growth condition $$\int_{B(0,r)}J_f(x)\,dx\leq c(1-r)^{-a} $$ for some a∈[0,n−1), then Open image in new window. Here the set E(f) consists of those points in ∂B(0,1) where f does not have radial limits. We also give an example which shows the difference between the classes of mappings of bounded distortion and certain integrable distortion in terms of radial limits.