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Search: MSC category 26A24 ( Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] )

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1. CMB 2011 (vol 54 pp. 706)

Moonens, Laurent
Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve
We provide a simple example showing that the tangential derivative of a continuous function $\phi$ can vanish everywhere along a curve while the variation of $\phi$ along this curve is nonzero. We give additional regularity conditions on the curve and/or the function that prevent this from happening.

Categories:26A24, 28A15

2. CMB 1998 (vol 41 pp. 497)

Borwein, J. M.; Girgensohn, R.; Wang, Xianfu
On the construction of Hölder and Proximal Subderivatives
We construct Lipschitz functions such that for all $s>0$ they are $s$-H\"older, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed H\"older and approximate subderivatives.

Keywords:Lipschitz functions, Hölder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, Hölder smooth, dyadic rationals
Categories:49J52, 26A16, 26A24

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