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We give a simple alternative proof for the $C^{1,1}$--convex extensionproblem 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-Whitneyproblem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provideexplicit formulae for the extensions. For the Gleaser-Whitney problem theobtained extension is almost minimal, that is, minimal up to a factor$\frac{1+\sqrt{3}}{2}$ in the sense of Le Gruyer [15].

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