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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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