We study the mappings of the Orlicz–Sobolev classes with a branching defined in the unit ball of the Euclidean space. We have obtained estimates for the distortion of the distance under these mappings at the points of the unit sphere. Under some conditions, we have also obtained the Hölder continuity of the mappings mentioned above. If we suppose that the considered mappings are solutions to certain Laplacian-gradient inequalities, we get the Lipschitz property. In section 7–9, we review some results, prove a new result, Theorem 7.1, and outline the proof of Theorem 9.2.

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