Universidad Complutense de Madrid
E-Prints Complutense

An Extension Theorem for convex functions of class C1,1 on Hilbert spaces

Impacto

Downloads

Downloads per month over past year

Azagra Rueda, Daniel and Mudarra, C. (2017) An Extension Theorem for convex functions of class C1,1 on Hilbert spaces. Journal of Mathematical Analysis and Applications, 446 (2). pp. 1167-1182. ISSN 0022-247X

[img]
Preview
PDF
190kB
[img] PDF
Restringido a Repository staff only

378kB

Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X16305182


URLURL Type
http://www.sciencedirect.com/Publisher


Abstract

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.


Item Type:Article
Uncontrolled Keywords:C1,1 function; Convex function; Whitney extension theorem
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:41483
Deposited On:27 Feb 2017 11:52
Last Modified:27 Feb 2017 12:20

Origin of downloads

Repository Staff Only: item control page