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# 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 $B={u\in W^{1,\infty}(Ømega)¸ |¸|\nabla u|^{2}\leq 1}¸.$
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https://hal.inria.fr/inria-00073499
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Submitted on : Wednesday, May 24, 2006 - 1:04:02 PM
Last modification on : Friday, February 4, 2022 - 3:22:55 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:48:08 PM

### Identifiers

• HAL Id : inria-00073499, version 1

### Citation

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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