On the smoothness of convex envelopes. (English) Zbl 0712.49010
The paper deals with differentiability properties of the convex envelope conv E of a lower semicontinuous function E: \(R^ n\to (- \infty,\infty]\), \(\lim_{| \delta | \to \infty}| \delta |^{-1}E(\delta)=\infty\) in terms of properties of E. Analogously to the known results on the regularity threshold for solutions to the obstacle problem conv E is not in general \(C^ 2\) even for analytic E. General conditions on E are given under which conv E inherits local \(C^{1,\alpha}\) regularity of E, \(0\leq \alpha \leq 1\).
Reviewer: M.Kokurin
MSC:
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 49J52 | Nonsmooth analysis |
| 26B05 | Continuity and differentiation questions |
References:
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