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1. 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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