Corrigendum: ``Inverse mean value property of harmonic functions''
The main statement of [Math. Ann. 297, 147-156 (1993; Zbl 0794.31001)] is the following: Let \(B\) denote an open ball in \(\mathbb{R}^d\), \(d \geq 2\), and let \(A\) be a measurable subset of \(\mathbb{R}^d\) having the same Lebesgue measure as \(B\). Then the average of \(h\) on \(A\) is equal to the value of \(h\) at the centre of \(B\) for every bounded \(h = (1_C - 1_D)* G\), \(C\) and \(D\) compact subsets of \(\complement A\) \((G = - \ln |\cdot |\) if \(d = 2\), \(G = |\cdot |^{2 - d}\) if \(d > 2)\), if and only if \(A\) and \(B\) differ by a Lebesgue null set. In the corrigendum an inequality in the first lemma is corrected and it is shown that a slight modification of the original proof leads to the result stated above.
scientific article; zbMATH DE number 840190