Correction to ``Unbounded quadrature domains in \({\mathbb{R}}^ n\) \((n{\geq{}}3)\)'' (Q1803643)

The statement in Lemma 1.5 in the author's paper [J. Anal. Math. 56, 281- 291 (1991; Zbl 0745.31003)] is not true. In fact, the function \(g(t)=t^ n\log^{-2}(t)\) is a counterexample to Lemma 1.5. The incorrect proof given there depends on the wrong assertion that \(\int^ \infty_{r'}(t\log^ nt)^{-1}dt\) is divergent for \(n\geq 2\). To save Theorem 1.4 we have to change the statement of Lemma 1.1. Namely, part (b) of Lemma 1.1 should read \[ |\nabla u(y)|\leq C\bigl[1+| y-\xi|\log\bigl({|\xi|\over| y- \xi|}\bigr)\bigr], \] where \(\xi\) is any point on \(\partial\Omega\).