# Calculating tangent sets to certain sets in functional spaces

Abstract : We give necessary and sufficient conditions for a given element to be a member of the second order tangent set $T»_{K}(f,v)$ to the positive cone $K$ in $L^{\infty}¸.$ Since, in general $T»_{K}(f,v)$ may be empty we give conditions on functions $f¸, v$ which ensure that the second tangent set is a cone. As an application of the results obtained we give a characterization of the elements of the first and second tangent set to the set $B={u\in W^{1,\infty}(Ømega)¸ |¸|\nabla u|^{2}\leq 1}¸.$
Keywords :
Type de document :
Rapport
[Research Report] RR-3190, INRIA. 1997, pp.24
Domaine :

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https://hal.inria.fr/inria-00073499
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 13:04:02
Dernière modification le : samedi 17 septembre 2016 - 01:06:51
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:48:08

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• HAL Id : inria-00073499, version 1

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Ewa Bednarczuk, Michel Pierre, Elisabeth Rouy, Jan Sokolowski. Calculating tangent sets to certain sets in functional spaces. [Research Report] RR-3190, INRIA. 1997, pp.24. 〈inria-00073499〉

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