Planar mappings of subexponentially integrable distortion -- integrability of distortion of inverses

TL;DR

This paper proves the optimal regularity for the distortion of inverse mappings with subexponentially integrable distortion, extending previous results to a broader class of mappings with logarithm-iterated integrability conditions.

Contribution

It generalizes the existing theorem on distortion regularity to mappings with logarithm-iterated subexponential integrability, providing a more comprehensive understanding.

Findings

Established optimal regularity for inverse distortion

Extended previous theorems to broader integrability classes

Generalized results to logarithm-iterated subexponential distortion

Abstract

We establish the optimal regularity for the distortion of inverses of mappings of finite distortion with logarithm-iterated style subexponentially integrable distortion, which generalizes the Theorem 1. of [J. Gill, Ann. Acad. Sci. Fenn. Math. 35 (2010), no. 1, 197--207].