English

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

Functional Analysis 2018-02-20 v2

Abstract

We give a simple alternative proof for the C1,1C^{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 C1,1C^{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 1+32\frac{1+\sqrt{3}}{2} in the sense of Le Gruyer [15].

Keywords

Cite

@article{arxiv.1706.01721,
  title  = {Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of 1-fields in Hilbert spaces},
  author = {Aris Daniilidis and Mounir Haddou and Erwan Le Gruyer and Olivier Ley},
  journal= {arXiv preprint arXiv:1706.01721},
  year   = {2018}
}