Rotation bounds for Hölder continuous homeomorphisms with integrable distortion

Abstract

We obtain sharp rotation bounds for the subclass of homeomorphisms $f:\mathbb{C}\to \mathbb{C}$ of finite distortion which have distortion function in $L_{loc}^p$, $p>1$, and for which a Hölder continuous inverse is available. The interest in this class is partially motivated by examples arising from fluid mechanics. Our rotation bounds hereby presented improve the existing ones, for which the Hölder continuity is not assumed. We also present examples proving sharpness.

16 pages; typos corrected after report from referee