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

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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Cited literature [23 references]

https://hal.archives-ouvertes.fr/hal-01530908
Contributor : Olivier Ley <>
Submitted on : Saturday, February 17, 2018 - 7:02:26 PM
Last modification on : Thursday, November 15, 2018 - 11:56:48 AM
Long-term archiving on : Tuesday, May 8, 2018 - 12:05:07 AM

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DHLL_appendix.pdf
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### Identifiers

• HAL Id : hal-01530908, version 2
• ARXIV : 1706.01721

### Citation

Aris Daniilidis, Mounir Haddou, Erwan Le Gruyer, Olivier Ley. Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of 1-fields in Hilbert spaces. 2018. ⟨hal-01530908v2⟩

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