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

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Azagra Rueda, Daniel y 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

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


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Resumen

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.


Tipo de documento:Artículo
Palabras clave:C1,1 function; Convex function; Whitney extension theorem
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:41483
Depositado:27 Feb 2017 11:52
Última Modificación:27 Feb 2017 12:20

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