The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables
[La propriété de Denjoy-Clarkson par rapport aux mesures de Hausdorff et le gradient des fonctions de plusieurs variables]
Zelený, Miroslav
Annales de l'Institut Fourier, Tome 58 (2008), p. 405-428 / Harvested from Numdam
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On construit une fonction différentiable f:R n →R (n≥2) telle que l’ensemble (∇f) -1 (B(0,1)) est non vide et sa dimension de Hausdorff est 1. C’est une réponse à une question posée par Z. Buczolich.

We construct a differentiable function f:R n →R (n≥2) such that the set (∇f) -1 (B(0,1)) is a nonempty set of Hausdorff dimension 1. This answers a question posed by Z. Buczolich.

Publié le : 2008-01-01
DOI : https://doi.org/10.5802/aif.2356
Classification:  26B05,  28A75
Mots clés: propriété de Denjoy-Clarkson, gradient, mesure de Hausdorff, jeu infini 
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     author = {Zelen\'y, Miroslav},
     title = {The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables},
     journal = {Annales de l'Institut Fourier},
     volume = {58},
     year = {2008},
     pages = {405-428},
     doi = {10.5802/aif.2356},
     zbl = {1154.26016},
     mrnumber = {2410378},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2008__58_2_405_0}
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Zelený, Miroslav. The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables. Annales de l'Institut Fourier, Tome 58 (2008) pp. 405-428. doi : 10.5802/aif.2356. http://gdmltest.u-ga.fr/item/AIF_2008__58_2_405_0/

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