Azagra Rueda, DanielMudarra, C.2023-06-172023-06-1720170022-247X10.1016/j.jmaa.2016.09.015https://hdl.handle.net/20.500.14352/17649Let H be a Hilbert space, E⊂H be an arbitrary subset and f:E→R, G:E→H be two functions. We give a necessary and sufficient condition on the pair (f,G) for the existence of a convex function F∈C1,1(H) such that F=f and ∇F=G on E. We also show that, if this condition is met, F can be taken so that Lip(∇F)=Lip(G). We give a geometrical application of this result, concerning interpolation of sets by boundaries of C1,1 convex bodies in H. Finally, we give a counterexample to a related question concerning smooth convex extensions of smooth convex functions with derivatives which are not uniformly continuous.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022247X16305182http://www.sciencedirect.com/restricted access517C11 functionConvex functionWhitney extension theoremAnálisis matemático1202 Análisis y Análisis Funcional