Second-order subgradients of
convex integral functionals
Authors:
Mohammed Moussaoui and Alberto Seeger
Journal:
Trans. Amer. Math. Soc. 351 (1999), 3687-3711
MSC (1991):
Primary 49J52, 28B20
DOI:
https://doi.org/10.1090/S0002-9947-99-02248-5
Published electronically:
March 1, 1999
MathSciNet review:
1487628
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The purpose of this work is twofold: on the one hand, we study the second-order behaviour of a nonsmooth convex function defined over a reflexive Banach space
. We establish several equivalent characterizations of the set
, known as the second-order subdifferential of
at
relative to
. On the other hand, we examine the case in which
is the functional integral associated to a normal convex integrand
. We extend a result of Chi Ngoc Do from the space
to a possible nonreflexive Banach space
. We also establish a formula for computing the second-order subdifferential
.
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Additional Information
Mohammed Moussaoui
Affiliation:
Department of Mathematics, University of Avignon, 33, rue Louis Pasteur, 84000 Avignon, France
Alberto Seeger
Affiliation:
Department of Mathematics, University of Avignon, 33, rue Louis Pasteur, 84000 Avignon, France
DOI:
https://doi.org/10.1090/S0002-9947-99-02248-5
Keywords:
Convex integral functional,
subdifferential,
second-order subdifferential,
Mosco convergence.
Received by editor(s):
June 10, 1996
Received by editor(s) in revised form:
March 13, 1997
Published electronically:
March 1, 1999
Article copyright:
© Copyright 1999
American Mathematical Society