Differentiability of convex envelopes

Bernd Kirchheim and Jan Kristensen

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Submission date: 06. Dec. 1999
Pages: 4
published in: Comptes rendus de l'Académie des Sciences / 1, 333 (2001) 8, p. 725-728 
DOI number (of the published article): 10.1016/S0764-4442(01)02117-6
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Abstract:
We present a simple proof for the existence and (Hölder) continuity of derivatives of convex envelopes for functions . Besides being much shorter than prior proofs in the literature, our method also weakens the previously used growth conditions from below to the best possible ones (of this general kind).