On the Holder property of mappings in domains and on boundaries

We study homeomorphisms and mappings with branching in domains of the Euclidean space. We establish pointwise Holder and Lipschitz properties of mappings whose characteristics satisfy a Dini-type condition or whose mean values over infinitesimal balls are finite at the corresponding points. Moreover, we find conditions on the complex coefficients of the Beltrami equations in the unit disk under which their homeomorphic solutions are Holder-continuous on the boundary. Keywords. Open discrete ring Q-mappings, Holder continuity, Lipschitz property.
1. Introduction The Lipschitz-type inequalities for quasiconformal mappings of a unit ball into itself were obtained in paper [1], see also books [2] and [3] and articles [4] and [5]. [...]