Kirchheim, Bernd; Kristensen, Jan Differentiability of convex envelopes. (English. Abridged French version) Zbl 1053.49013 C. R. Acad. Sci., Paris, Sér. I, Math. 333, No. 8, 725-728 (2001). 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. Cited in 26 Documents 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 Keywords:convex envelopes; extended real-valued functions; semidifferentiability; \(C^1\)-regularity PDFBibTeX XMLCite \textit{B. Kirchheim} and \textit{J. Kristensen}, C. R. Acad. Sci., Paris, Sér. I, Math. 333, No. 8, 725--728 (2001; Zbl 1053.49013) Full Text: DOI