A relaxation result for autonomous integral functionals with discontinuous non-coercive integrand
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 201-210.

Let L: N × N be a borelian function and consider the following problems

infF(y)= a b L(y(t),y ' (t))dt:yAC([a,b], N ),y(a)=A,y(b)=B(P)
infF ** (y)= a b Ł(y(t),y ' (t))dt:yAC([a,b], N ),y(a)=A,y(b)=B·(P ** )
We give a sufficient condition, weaker then superlinearity, under which infF=infF ** if L is just continuous in x. We then extend a result of Cellina on the Lipschitz regularity of the minima of (P) when L is not superlinear.

DOI : 10.1051/cocv:2004004
Classification : 37N35
Mots clés : Lipschitz, regularity, non-coercive, discontinuous, calculus of variations
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     title = {A relaxation result for autonomous integral functionals with discontinuous non-coercive integrand},
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Mariconda, Carlo; Treu, Giulia. A relaxation result for autonomous integral functionals with discontinuous non-coercive integrand. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 201-210. doi : 10.1051/cocv:2004004. http://www.numdam.org/articles/10.1051/cocv:2004004/

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