Heriot-Watt Mathematics Report Series
HWM01-39, 11 Dec 2001
Differentiability of convex envelopes
B Kirchheim and J Kristensen
Abstract
We prove that the convex envelope of a differentiable (resp.
$C^{1,\alpha}$) function $f$ is $C^1$ (resp. $C^{1,\alpha}$) provided
only that $f(x) \to \infty$ as $|x| \to \infty$.
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