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Article

Pavlica, David
On the points of non-differentiability of convex functions. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 45 (2004), issue 4, pp. 727-734
MSC: 26B05, 26B25, 49J50, 49J52 | MR 2103086 | Zbl 1100.26006
Keywords:
differentiability; convex functions
Summary:
We characterize sets of non-differentiability points of convex functions on $\Bbb R^n$. This completes (in $\Bbb R^n$) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.
References:
[1] Rockafellar R.T.: Convex Analysis. Princeton University Press (1970). MR 0274683 | Zbl 0193.18401
[2] Zajíček L.: On the differentiability of convex functions in finite and infinite dimensional spaces. Czechoslovak Math. J. 29 (104) (1979), 340-348. MR 0536060
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