Geodesic
A d.c. $C^1$ function need not be difference of convex $C^1$ functions
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 1, pp. 75-83 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In [2] a delta convex function on $\Bbb R^2$ is constructed which is strictly differentiable at $0$ but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class $C^1(\Bbb R^2)$ which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.
In [2] a delta convex function on $\Bbb R^2$ is constructed which is strictly differentiable at $0$ but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class $C^1(\Bbb R^2)$ which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.
Classification : 26B05, 26B25
Keywords: differentiability; delta-convex functions 
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     author = {Pavlica, David},
     title = {A d.c. $C^1$ function need not be difference  of convex $C^1$ functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {75--83},
     year = {2005},
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Pavlica, David. A d.c. $C^1$ function need not be difference  of convex $C^1$ functions. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 1, pp. 75-83. http://geodesic.mathdoc.fr/item/CMUC_2005_46_1_a6/