论文标题
Hölder和Lipschitz在Orlicz-Sobolev类中的连续性，失真和谐波映射
Hölder and Lipschitz continuity in Orlicz-Sobolev classes, distortion and harmonic mappings
论文作者
论文摘要
在本文中，我们考虑了单位球上定义的Orlicz-Sobolev类中注射图的Hölder连续性。在扩张生长的某些条件下，我们获得了指定映射类别的Hölder连续性。特别是，在某些特殊限制下，我们表明Lipschitz的映射连续性存在。我们还考虑了谐波映射的Hölder和Lipschitz连续性，尤其是Orlicz-Sobolev类中的谐波映射。此外，在平面案例中，我们在某些情况下表明，如果Beltrami系数是Hölder连续的，则该地图是Bi-Lipschitzian。
In this article, we consider the Hölder continuity of injective maps in Orlicz-Sobolev classes defined on the unit ball. Under certain conditions on the growth of dilatations, we obtain the Hölder continuity of the indicated class of mappings. In particular, under certain special restrictions, we show that Lipschitz continuity of mappings holds. We also consider Hölder and Lipschitz continuity of harmonic mappings and in particular of harmonic mappings in Orlicz-Sobolev classes. In addition in planar case, we show in some situations that the map is bi-Lipschitzian if Beltrami coefficient is Hölder continuous.
