$C^1$-extension and $C^1$-reflection of subharmonic functions from Lyapunov-Dini domains into $\mathbb R^N$

If $D$ is a Lyapunov-Dini domain in $\mathbb R^N$, $N\in\{2,3,\dots\}$, the possibility of $C^1$-extension and $C^1$-reflection of subharmonic functions in $D$ lying in the class $C^1(\overline D)$ across the boundary of $D$ to the whole of $\mathbb R^N$ is investigated. In particular, it is shown that extensions and reflections of this kind are always possible for an arbitrary Lyapunov domain with connected complement.
Bibliography: 14 titles.