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MiS Preprint
68/1999
Differentiability of convex envelopes
Bernd Kirchheim and Jan Kristensen
Abstract
We present a simple proof for the existence and (Hölder) continuity of derivatives of convex envelopes for functions $f:\mathbb{R}^n \to \mathbb{R}\cup \{+\infty\}$. 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).
