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On the Clarke subdifferential of an integral functional on $L_p$, $1\leq p < \infty$

Published:1998-03-01
Printed: Mar 1998
• E. Giner
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Abstract

Given an integral functional defined on $L_p$, $1 \leq p <\infty$, 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: Integral functional, integrand, epi-derivative
 MSC Classifications: 28A25 - Integration with respect to measures and other set functions 49J52 - Nonsmooth analysis [See also 46G05, 58C50, 90C56] 46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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