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We study the relations between the Lipschitz constant of $1$-field and theLipschitz constant of the gradient canonically associated with this $1$-field.Moreover, we produce two explicit formulas that make up Minimal Lipschitzextensions for $1$-field. As consequence of the previous results, for theproblem of minimal extension by continuous functions from $\mathbb{R}^m$ to$\mathbb{R}^n$, we also produce analogous explicit formulas to those ofBauschke and Wang. Finally, we show that Wells's extensions of $1$-field areabsolutely minimal Lipschitz extension when the domain of $1$-field to expandis finite. We provide a counter-example showing that this result is false ingeneral.

Some results of the Lipschitz constant of 1-Field on $\mathbb{R}^n$