Harmonic monsters.
Using a theorem of \textit{S. J. Gardiner} [Harmonic approximation (1995; Zbl 0826.31002)], the author shows that there exists a harmonic function \(h\) on a non-empty open subset \(\Omega\) of \(\mathbb{R}^d\), where \(d\geq 2\), which behaves wildly near every boundary point of \(\Omega\). The function \(h\) is analogous to the holomorphic monster function of \textit{W. Luh} [J. Approximation Theory 53, No. 2, 128--144 (1988; Zbl 0669.30020)]. The author also compares his result with that of Luh's and obtains some improvements of his main result.
scientific article; zbMATH DE number 1957011