%0 Journal Article
%T Radial representation of lower semicontinuous envelope
%+ Laboratoire de Mécanique et Génie Civil (LMGC)
%+ Mathématiques et Modélisations en Mécanique (M3)
%+ Mathématiques, Informatique, Physique, et Applications / Université de Nîmes (MIPA)
%A Anza Hafsa, Omar
%A Mandallena, Jean-Philippe
%< avec comité de lecture
%@ 1972-6724
%J Bollettino dell'Unione Matematica Italiana
%I Springer Verlag
%V 7
%N 1
%P 1-18
%8 2014-03
%D 2014
%Z 1211.6504
%R 10.1007/s40574-014-0001-1
%K Ru-usc functions
%K Relaxation with constraints
%K Radial representation
%K Star-shaped set
%K Extension on the boundary
%Z Mathematics [math]/Classical Analysis and ODEs [math.CA]Journal articles
%X We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper semicontinuity which plays the role of convexity, and allows to prove a radial representation result for nonconvex functions. An application to the relaxation of multiple integrals with constraints on the gradient is given.
%G English
%2 https://hal.science/hal-00958312/document
%2 https://hal.science/hal-00958312/file/Anza_Mandallena_Radial_representation_Boll.Uni.Math.Ita._2014.pdf
%L hal-00958312
%U https://hal.science/hal-00958312
%~ CNRS
%~ LMGC
%~ UNIMES
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021