×

Differentiability of convex envelopes. (English. Abridged French version) Zbl 1053.49013

Summary: We prove that the convex envelope of a differentiable function (or \(C^{1,\alpha}\)-function) \(f\) is \(C^1\) (or \(C^{1,\alpha})\), respectively, provided only that the function satisfies the very mild growth condition that \(f(x)\) tends to \(+\infty\) if \(| x|\) does so.

MSC:

49J52 Nonsmooth analysis
49J10 Existence theories for free problems in two or more independent variables
26B25 Convexity of real functions of several variables, generalizations
PDFBibTeX XMLCite
Full Text: DOI