In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set we construct a differentiable function for which there exists an open set such that for a but for almost every . This shows that the Denjoy-Clarkson property does not hold in higher dimensions.
Cite this article
Zoltán Buczolich, Solution to the gradient problem of C. E. Weil. Rev. Mat. Iberoam. 21 (2005), no. 3, pp. 889–910DOI 10.4171/RMI/439