Geodesic
On the Construction of Hölder and Proximal Subderivatives
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 497-507

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DOI

We construct Lipschitz functions such that for all $s>0$ they are $s$ -Hölder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Hölder and approximate subderivatives.
DOI : 10.4153/CMB-1998-065-9
Mots-clés : 49J52, 26A16, 26A24, Lipschitz functions, Hölder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, Hölder smooth, dyadic rationals 
Borwein, J. M.; Girgensohn, R.; Wang, Xianfu. On the Construction of Hölder and Proximal Subderivatives. Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 497-507. doi: 10.4153/CMB-1998-065-9
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     author = {Borwein, J. M. and Girgensohn, R. and Wang, Xianfu},
     title = {On the {Construction} of {H\"older} and {Proximal} {Subderivatives}},
     journal = {Canadian mathematical bulletin},
     pages = {497--507},
     year = {1998},
     volume = {41},
     number = {4},
     doi = {10.4153/CMB-1998-065-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-065-9/}
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