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Intégration Du Sous-Différentiel Proximal: Un Contre Exemple

Published online by Cambridge University Press:  20 November 2018

Joël Benoist
Joël Benoist*
Affiliation:
Département de Mathématiques Faculté des Sciences 123, rue Albert Thomas 87060 Limoges France, e-mail: benoist@cict.fr
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Résumé

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Etant donnée une partie $D$ dénombrable et dense de $\mathbb{R}$, nous construisons une infinité de fonctions Lipschitziennes définies sur $\mathbb{R}$, s'annulant en zéro, dont le sous-différentiel proximal est égal à ]–1, 1[ en tout point de $D$ et est vide en tout point du complémentaire de $D$. Nous déduisons que deux fonctions dont la différence n'est pas constante peuvent avoir les mêmes sous-différentiels.

Keywords

26A1626A24
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 2 , 01 April 1998 , pp. 242 - 265
Copyright
Copyright © Canadian Mathematical Society 1998

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