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arXiv · 1706.01721

Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of 1-fields in Hilbert spaces

Aris Daniilidis·Mounir Haddou·Erwan Le Gruyer·Olivier Ley
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Abstract

We give a simple alternative proof for the $C^{1,1}$--convex extension problem which has been introduced and studied by D. Azagra and C. Mudarra [2]. As an application, we obtain an easy constructive proof for the Glaeser-Whitney problem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provide explicit formulae for the extensions. For the Gleaser-Whitney problem the obtained extension is almost minimal, that is, minimal up to a factor $\frac{1+\sqrt{3}}{2}$ in the sense of Le Gruyer [15].

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Aris Daniilidis, Mounir Haddou, Erwan Le Gruyer, Olivier Ley. 2017-06-06. Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of 1-fields in Hilbert spaces. https://arxiv.org/abs/1706.01721

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