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On the Clarke Subdifferential of an Integral Functional on Lp, 1 ≤ p < ∞

Published online by Cambridge University Press:  20 November 2018

E. Giner
E. Giner*
Affiliation:
Laboratoire Approximation et Optimisation Université Paul Sabatier 118, route de Narbonne 31062 Toulouse France
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Abstract

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Given an integral functional defined on ${{L}_{p}}$, $1\le p<\infty $, under a growth condition we give an upper bound of the Clarke directional derivative and we obtain a nice inclusion between the Clarke subdifferential of the integral functional and the set of selections of the subdifferential of the integrand.

Keywords

28A2549J5246E30Integral functionalintegrandepi-derivative
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 1 , 01 March 1998 , pp. 41 - 48
Copyright
Copyright © Canadian Mathematical Society 1998

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