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1996/1997 Another note on the gradient problem of C. E. Weil
Zoltán Buczolich
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Real Anal. Exchange 22(2): 775-784 (1996/1997).


Assume that \(G\subset \mathbb{R}^n\) is open and \(f:G\to\mathbb{R}\) is a differentiable function. C. E. Weil raised the gradient problem. In this problem it is asked whether \(\triangledown f\) satisfies the natural multidimensional generalization of the Denjoy-Clarkson property. We verify that if there are two dimensional counterexample functions to the gradient problem then their range should satisfy certain paradoxical convexity properties and the inverse image of ``many" values of \(\triangledown f\) is of positive linear measure.


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Zoltán Buczolich. "Another note on the gradient problem of C. E. Weil." Real Anal. Exchange 22 (2) 775 - 784, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 22 May 2012

zbMATH: 0940.26011
MathSciNet: MR1460988

Primary: 26B24

Keywords: gradient problem

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 2 • 1996/1997
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