Localized regularity of planar maps of finite distortion

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion. Analogues of such results were known earlier in the case of quasiconformal mappings. Moreover, we study regularity for maps whose distortion has higher exponential integrability.