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2002/2003 Gâteaux differentiability of Lipschitz functions via directional derivatives.
A. Nekvinda, L. Zajíček
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Real Anal. Exchange 28(2): 287-320 (2002/2003).


Let \(X\) be a separable Banach space, \(Y\) a Banach space and \(f:X \to Y\) a Lipschitz function. We show that the set of all G\^ ateaux non-differentiability points at which \(f\) has all one-sided or two-sided directional derivatives can be covered by (special subsets of) Lipschitz surfaces of codimension 1 or codimension 2, respectively. Further results indicate that these results are close to the best possible ones. Our results are new also for Lipschitz functions \(\R^n \to \R\); for these functions G\^ ateaux differentiability is the classical (total) differentiability.


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A. Nekvinda. L. Zajíček. "Gâteaux differentiability of Lipschitz functions via directional derivatives.." Real Anal. Exchange 28 (2) 287 - 320, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

zbMATH: 1049.49018
MathSciNet: MR2009756

Primary: 26B05
Secondary: 46G05

Keywords: directional derivative , G\^ateaux differentiability , Lipschitz function , Lipschitz surface , Separable Banach space

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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