A Characterization of Harmonic Arakelyan Sets
M. Goldstein, Wellington H. Ow · Proceedings of the American Mathematical Society · 1993
Given a closed subset $F$ of either ${R^N},\;N \geqslant 3$, or a Riemann surface, necessary and sufficient conditions are given so that every function continuous on $F$ and harmonic in the interior can be uniformly approximated on $F$ by globally defined harmonic functions.