Resumen de Solution to the gradient problem of C. E. Weil

Zoltán Buczolich

• In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G Ì R2 we construct a differentiable function f: G ? R for which there exists an open set O1 Ì R2 such that Ñf(p) Î O1 for a p Î G but Ñf(q) Ï O1 for almost every q Î G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.