No abstract

We generalize to Hilbert spaces a theorem of Glaeser concerning minimal Lipschitz extensions of m-jets of one variable with range in R. The results contained in this paper can be seen as a small contribution to the general problem of the minimal Lipschitz extensions from m-jets for a Hilbert space to another Hilbert space.

We study the relations between the Lipschitz constant of 1-field introduced in [12] and the Lipschitz constant of the gradient canonically associated with this 1-field. Moreover, we produce two explicite formulas that make up Minimal Lipschitz extensions for 1-field. As consequence of the previous results, for the problem of minimal extension by continuous functions from R m to R n , we also produce analogous explicite formulas to those of Bauschke and Wang (see [6]). Finally, we show that Wells's extensions of 1-field are absolutely minimal Lipschitz extension when the domain of 1-field to expand is finite. We provide a counter-example showing that this result is false in general.