Geodesic
$C^1$-extension and $C^1$-reflection of subharmonic functions from Lyapunov-Dini domains into
Sbornik. Mathematics, Tome 199 (2008) no. 12, pp. 1809-1846

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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. 
@article{SM_2008_199_12_a3,
     author = {P. V. Paramonov},
     title = {$C^1$-extension and $C^1$-reflection of subharmonic functions from {Lyapunov-Dini} domains into},
     journal = {Sbornik. Mathematics},
     pages = {1809--1846},
     publisher = {mathdoc},
     volume = {199},
     number = {12},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_12_a3/}
}
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P. V. Paramonov. $C^1$-extension and $C^1$-reflection of subharmonic functions from Lyapunov-Dini domains into. Sbornik. Mathematics, Tome 199 (2008) no. 12, pp. 1809-1846. http://geodesic.mathdoc.fr/item/SM_2008_199_12_a3/