On Hölder continuity of mappings in domains and on boundaries

Abstract

We study mappings with branching of a domain of Euclidean space. The Hölder and Lipschitz continuity are established for one class of spatial mappings whose characteristic satisfies the Dini type condition in a given domain. In addition, we found conditions on the complex coefficient of the degenerate Beltrami equations in the unit disk under which generalized homeomorphic solutions of this equation are Hölder continuous at the points of the boundary.