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We study mappings with branching of a domain of Euclidean space. The H\"olderand Lipschitz continuity are established for one class of spatial mappingswhose characteristic satisfies the Dini type condition in a given domain. Inaddition, we found conditions on the complex coefficient of the degenerateBeltrami equations in the unit disk under which generalized homeomorphicsolutions of this equation are H\"older continuous at the points of theboundary.

On H\"older continuity of mappings in domains and on boundaries