TY - JOUR
AU - E. A. Sevost'yanov
PY - 2016/05/25
Y2 - 2020/09/25
TI - On the removability of isolated singularities of Orlicz – Sobolev classes with branching
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 68
IS - 5
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1871
AB - The local behavior of closed-open discrete mappings of the Orlicz – Sobolev classes in $R^n,\; n \geq 3$, is investigated. It is proved that the indicated mappings have continuous extensions to an isolated boundary point $x_0$ of the domain $D \setminus \{ x0\}$,whenever the $n - 1$ degree of its inner dilatation has FMO (finite mean oscillation) at this point and, in addition, the limit sets of $f$ at $x_0$ and $\partial D$ are disjoint. Another sufficient condition for the possibility of continuous extension can beformulated as a condition of divergence of a certain integral.
ER -