  We study mappings with branching of a domain of Euclidean space. The H\"older
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 H\"older continuous at the points of the
boundary.
