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

Revista Matemática Iberoamericana (2005)

- Volume: 21, Issue: 3, page 889-910
- ISSN: 0213-2230

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topBuczolich, Zoltán. "Solution to the gradient problem of C.E. Weil.." Revista Matemática Iberoamericana 21.3 (2005): 889-910. <http://eudml.org/doc/41954>.

@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 -