1. CMB 2011 (vol 54 pp. 706)
|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.
2. CMB 1998 (vol 41 pp. 497)
|On the construction of HÃ¶lder 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, HÃ¶lder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, HÃ¶lder smooth, dyadic rationals
Categories:49J52, 26A16, 26A24