Wee-Kee Tang
On Fr\'echet differentiability of convex functions on Banach spaces

Comment.Math.Univ.Carolinae 36,2 (1995) 249-253.

Abstract:Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function $f$ defined on a separable Banach space are studied. The conditions are in terms of a majorization of $f$ by a $C^1$-smooth function, separability of the boundary for $f$ or an approximation of $f$ by Fr\'echet smooth convex functions.

Keywords: Fr\'echet differentiability, convex functions, variational principles, Asplund spaces
AMS Subject Classification: 46B03