A note on the differentiability of conjugate functions (Q1042426)

The following extension of Rockafellar's fundamental theorem is proved: Let \(f:\mathbb{R}^n\to\overline{\mathbb{R}}\) be a proper, lower semicontinuous function such that its conjugate \(f^{\ast}\) is proper. Then \(f^{\ast}\) is essentially differentiable if and only if \(f\) is essentially strictly convex.