### Impacto

### Downloads

Downloads per month over past year

Azagra Rueda, Daniel and Mudarra, C.
(2017)
*Whitney extension theorems for convex functions of the classes C1 and C1ω.*
Proceedings of the London Mathematical Society, 114
(1).
pp. 133-158.
ISSN 0024-6115

PDF
Restringido a Repository staff only 350kB |

Official URL: http://onlinelibrary.wiley.com/doi/10.1112/plms.12006/full

## Abstract

Let C be a subset of ℝn (not necessarily convex), f : C → R be a function and G : C → ℝn be a uniformly continuous function, with modulus of continuity ω. We provide a necessary and sufficient condition on f, G for the existence of a convex function F ∈ CC1ω(ℝn) such that F = f on C and ∇F = G on C, with a good control of the modulus of continuity of ∇F in terms of that of G. On the other hand, assuming that C is compact, we also solve a similar problem for the class of C1 convex functions on ℝn, with a good control of the Lipschitz constants of the extensions (namely, Lip(F) ≲ ∥G∥∞). Finally, we give a geometrical application concerning interpolation of compact subsets K of ℝn by boundaries of C1 or C1,1 convex bodies with prescribed outer normals on K.

Item Type: | Article |
---|---|

Additional Information: | [final page numbers not yet available] |

Subjects: | Sciences > Mathematics > Differential geometry |

ID Code: | 43806 |

Deposited On: | 11 Jul 2017 08:11 |

Last Modified: | 11 Jul 2017 10:23 |

### Origin of downloads

Repository Staff Only: item control page