Solution to the gradient problem of C. E. Weil

• Autores: Zoltán Buczolich
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 21, Nº 3, 2005, págs. 889-910
• Idioma: inglés
• DOI: 10.4171/rmi/439
• Títulos paralelos:
  • Solución al problema del gradiente de C.E. Weil.
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.