Sup-Inf explicit formulas for minimal Lipschitz extensions for 1-fields on Rn

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:424

Article

Le Gruyer, Erwan Y.¹ 

[1] INSA Rennes, F-35708 Rennes 7, France

关键词: Minimal;    Lipschitz;    Extension;    Differentiable function;    Convex analysis;   

DOI  :  10.1016/j.jmaa.2014.11.067

来源: Elsevier

【 摘 要 】

We study the relationship between the Lipschitz constant of 1-field introduced in [12] and the Lipschitz constant of the gradient canonically associated with this 1-field. Moreover, we produce two explicit formulas which are two extremal minimal Lipschitz extensions for 1-fields. As a consequence of the previous results, for the problem of minimal extension by Lipschitz continuous functions from R-m to R-n, we produce explicit formilins similar to those of Bauschke and Wang (see [7]). Finally, we show that Wells's extensions (see [24]) of 1-fields are absolutely minimal Lipschitz extensions when the domain of 1-field to expand is finite. We provide a counter-example showing that this result is false in general. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free