Geodesic
Necessary Conditions for Differentiability of Distance Functions
Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 815-820.

Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained. 
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V. S. Balaganskii. Necessary Conditions for Differentiability of Distance Functions. Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 815-820. http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a2/

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