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

@article{Buczolich2005,
abstract = {In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R2 we construct a differentiable function f: G → R for which there exists an open set Ω1 ⊂ R2 such that ∇f(p) ∈ Ω1 for a p ∈ G but ∇f(q) ∉ Ω1 for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.},
author = {Buczolich, Zoltán},
journal = {Revista Matemática Iberoamericana},
keywords = {Funciones diferenciables; Gradientes; Teoría de la medida; Denjoy-Clarkson property; Lebesgue measure},
language = {eng},
number = {3},
pages = {889-910},
title = {Solution to the gradient problem of C.E. Weil.},
url = {http://eudml.org/doc/41954},
volume = {21},
year = {2005},
}

TY - JOUR
AU - Buczolich, Zoltán
TI - Solution to the gradient problem of C.E. Weil.
JO - Revista Matemática Iberoamericana
PY - 2005
VL - 21
IS - 3
SP - 889
EP - 910
AB - In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R2 we construct a differentiable function f: G → R for which there exists an open set Ω1 ⊂ R2 such that ∇f(p) ∈ Ω1 for a p ∈ G but ∇f(q) ∉ Ω1 for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.
LA - eng
KW - Funciones diferenciables; Gradientes; Teoría de la medida; Denjoy-Clarkson property; Lebesgue measure
UR - http://eudml.org/doc/41954
ER -