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1. CMB 2011 (vol 54 pp. 706)
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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)
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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 |