Distinct differentiable functions may share the same Clarke subdifferential at all points

Borwein, J.; Wang, Xianfu

doi:10.1090/S0002-9939-97-03654-X

Distinct differentiable functions may share the same Clarke subdifferential at all points
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by J. M. Borwein and Xianfu Wang PDF

Proc. Amer. Math. Soc. 125 (1997), 807-813 Request permission

Abstract:

We construct, using Zahorski’s Theorem, two everywhere differentiable real–valued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential.

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