RT Journal Article
T1 An Extension Theorem for convex functions of class C1,1 on Hilbert spaces
A1 Azagra Rueda, Daniel
A1 Mudarra, C.
AB Let 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.
PB Elsevier
SN 0022-247X
YR 2017
FD 2017
LK https://hdl.handle.net/20.500.14352/17649
UL https://hdl.handle.net/20.500.14352/17649
LA eng
NO Ministerio de Economía y Competitividad (MINECO)
DS Docta Complutense
RD 7 jun 2025