All convex bodies are in the subdifferential of some everywhere differentiable locally Lipschitz function

We construct a differentiable locally Lipschitz function f$f$ in RN$\mathbb {R}^{N}$ with the property that for every convex body K⊂RN$K\subset \mathbb {R}^N$ there exists x¯∈RN$\bar{x} \in \mathbb {R}^N$ such that K$K$ coincides with the set ∂Lf(x¯)$\partial _L f(\bar{x})$ of limits of derivatives...

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Bibliographic Details

Published in:	Proceedings of the London Mathematical Society Vol. 129; no. 5
Main Authors:	Daniilidis, Aris, Deville, Robert, Tapia‐García, Sebastián
Format:	Journal Article
Language:	English
Published:	London Mathematical Society 01.11.2024
Subjects:	Classical Analysis and ODEs Functional Analysis Mathematics Optimization and Control Differentiable Lipschitz function subdifferential range Differentiable Lipschitz function subdifferential range convex body spaceability AMS Subject Classification Primary 26A30 49J52 49J52 Secondary 26A24 26A16 26A27 spaceability spaceability AMS Subject Classification Primary 26A30 Secondary 26A24 26A16 26A27 convex body
ISSN:	0024-6115, 1460-244X
Online Access:	Get full text
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