分支Orlicz-Sobolev类的孤立奇点的可去性
On removability of isolated singularities of Orlicz-Sobolev classes with branching
摘要：
研究了${\Bbb R}^n,$ $n\ge 3,$中Orlicz-Sobolev类闭开离散映射的一个局部性态.证明了当区域$D\setminus\{x_0\}$的内膨胀度$n-1$在孤立边界点$x_0$上有有限平均振荡时，上述映射对该点有连续扩张，且$f$在$x_0$和$\partial D$上的极限集不相交.连续扩张可能性的另一个充分条件是某个积分的发散
英文摘要：
A local behavior of closed open discrete mappings of Orlicz--Sobolev classes in ${\Bbb R}^n,$ $n\ge 3,$ is studied. It is proved that, mappings mentioned above have continuous extension to isolated boundary point $x_0$ of a domain $D\setminus\{x_0\}$ whenever $n-1$ degree of its inner dilatation has $FMO$ (finite mean oscillation) at the point and, besides that, limit sets of $f$ at $x_0$ and $\partial D$ are disjoint. Another sufficient condition of possibility of continuous extension is a divergence of some integral
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