M. Aschenbrenner and A. Fischer, Definable versions of theorems by Kirszbraun and Helly, Proc. Lond, pp.468-502, 2011.
DOI : 10.1112/plms/pdq029

URL : http://arxiv.org/abs/0906.1168

D. Azagra and C. Mudarra, An Extension Theorem for convex functions of class C1,1 on Hilbert spaces, Journal of Mathematical Analysis and Applications, vol.446, issue.2, pp.1167-1182, 2017.
DOI : 10.1016/j.jmaa.2016.09.015

D. Azagra and C. Mudarra, Whitney extension theorems for convex functions of the classes C 1 and C 1, Proc. Lond, pp.133-158, 2017.

E. N. Barron, P. Cannarsa, R. Jensen, and C. Sinestrari, Regularity of Hamilton-Jacobi equations when forward is backward, Indiana University Mathematics Journal, vol.48, issue.2, pp.385-409, 1999.
DOI : 10.1512/iumj.1999.48.1647

URL : http://doi.org/10.1512/iumj.1999.48.1647

H. Bauschke and X. Wang, Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theory, Contemp. Math, vol.513, pp.55-64, 2010.
DOI : 10.1090/conm/513/10075

URL : http://arxiv.org/abs/0807.1257

J. M. Borwein and C. H. Hamilton, Symbolic Fenchel Conjugation, Mathematical Programming, pp.17-35, 2009.
DOI : 10.1007/s10107-007-0134-4

Y. Brudnyi and P. Shvartsman, Whitney's extension problem for multivariate C 1,? -functions, Transactions of the American Mathematical Society, vol.353, issue.06, pp.2487-2512, 2001.
DOI : 10.1090/S0002-9947-01-02756-8

P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations, and optimal control, Progress in Nonlinear Differential Equations and their Applications, 2004.

C. Fefferman, A sharp form of Whitney???s extension theorem, Annals of Mathematics, vol.161, issue.1, pp.509-577, 2005.
DOI : 10.4007/annals.2005.161.509

C. Fefferman, A. I. , and G. Luli, Finiteness Principles for Smooth Selection, Geometric and Functional Analysis, vol.9, issue.3, 2016.
DOI : 10.1007/s00039-016-0366-7

URL : http://arxiv.org/abs/1511.04804

C. Fefferman, A. Israel, and G. Luli, Interpolation of data by smooth nonnegative functions, Revista Matem??tica Iberoamericana, vol.33, issue.1, pp.305-324, 2017.
DOI : 10.4171/RMI/938

]. G. Glaeser, ??tude de Quelques Alg??bres Tayloriennes, Journal d'Analyse Math??matique, vol.245, issue.1, pp.1-124, 1958.
DOI : 10.1007/BF02790231

A. Herbert-voss, M. J. Hirn, and F. Mccollum, Computing minimal interpolants in $C^{1,1}(\mathbb R^d)$, Revista Matem??tica Iberoamericana, vol.33, issue.1, pp.29-66, 2017.
DOI : 10.4171/RMI/927

URL : http://arxiv.org/abs/1411.5668

J. Lasry and P. Lions, A remark on regularization in Hilbert spaces, Israel Journal of Mathematics, vol.92, issue.134, pp.257-266, 1986.
DOI : 10.1007/BF02765025

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA149046

E. and L. Gruyer, Minimal Lipschitz Extensions to Differentiable Functions Defined on a Hilbert Space, Geometric and Functional Analysis, vol.36, issue.1, pp.1101-1118, 2009.
DOI : 10.1007/s00039-009-0027-1

URL : https://hal.archives-ouvertes.fr/hal-00456975

E. , L. Gruyer, and T. V. Phan, Sup-inf explicit formulas for minimal Lipschitz extensions for 1-fields on R n, J. Math. Anal. Appl, vol.424, issue.2, pp.1161-1185, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01113015

C. Lemaréchal and C. Sagastizábal, Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries, SIAM Journal on Optimization, vol.7, issue.2, pp.367-385, 1997.
DOI : 10.1137/S1052623494267127

Y. Lucet, Fast Moreau envelope computation I: numerical algorithms, Numerical Algorithms, vol.17, issue.153, pp.235-249, 2006.
DOI : 10.1007/s11075-006-9056-0

E. J. Mcshane, Extension of range of functions, Bulletin of the American Mathematical Society, vol.40, issue.12, pp.837-842, 1934.
DOI : 10.1090/S0002-9904-1934-05978-0

F. A. Valentine, A Lipschitz Condition Preserving Extension for a Vector Function, American Journal of Mathematics, vol.67, issue.1, pp.83-93, 1945.
DOI : 10.2307/2371917

J. C. Wells, Differentiable functions on Banach spaces with Lipschitz derivatives, Journal of Differential Geometry, vol.8, issue.1, pp.135-152, 1973.
DOI : 10.4310/jdg/1214431488

H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Transactions of the American Mathematical Society, vol.36, issue.1, pp.63-89, 1934.
DOI : 10.1090/S0002-9947-1934-1501735-3

N. Zobin, Whitney's Problem on Extendability of Functions and an Intrinsic Metric, Advances in Mathematics, vol.133, issue.1, pp.96-132, 1998.
DOI : 10.1006/aima.1997.1685