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On the second differentiability of convex surfaces

✍ Scribed by Gabriele Bianchi; Andrea Colesanti; Carlo Pucci

Publisher
Springer
Year
1996
Tongue
English
Weight
493 KB
Volume
60
Category
Article
ISSN
0046-5755

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✦ Synopsis

Properties of pointwise second differentiability of real-valued convex functions in ~ ' ~ are studied. Some proofs of the Busemann-Feller-Aleksandrov theorem are reviewed and a new proof of this theorem is presented.

πŸ“œ SIMILAR VOLUMES

Generic FrΓ©chet Differentiability of Con
Generic FrΓ©chet Differentiability of Convex Functions on Non-Asplund Spaces
✍ Cheng Lixin; Shi Shuzhong; E.S. Lee πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 204 KB

Let f be a continuous convex function on a Banach space E. This paper shows that every proper convex function g on E with g F f is generically Frechet differentiable if and only if the image of the subdifferential map Ѩ f of f has the Radon᎐Nikodym property, and in this case it is equivalent to show