On the Behavior of Orlicz–Sobolev Mappings with Branching on the Unit Sphere

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