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Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions

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Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions ANNALES DE L’I. H. P., SECTION C ARRIGO CELLINA FABIÁN FLORES Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions Annales de l’I. H. P., section C, tome 9, no 4 (1992), p. 465-477. <http://www.numdam.org/item?id=AIHPC_1992__9_4_465_0> © Gauthier-Villars, 1992, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section C » (http://www.elsevier.com/locate/anihpc), implique l’accord avec les condi- tions générales d’utilisation (http://www.numdam.org/legal.php). Toute uti- lisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions Arrigo CELLINA and Fabián FLORES S.I.S.S.A., Strada Costiera 11, 34014 Trieste, Italy Ann. Inst. Henri Poincaré, Vol. 9, n° 4, 1992, p. 465-478. Analyse non linéaire ABSTRACT. - We show that the functional attains a minimum on the space W6’ P (B). Key words : Calculus of Variations, convex functionals, rotation group, radially symmetric solutions. RESUME. 2014 Nous montrons que le fonctionnel atteint le minimum sur l’espace W6’ P (B). . - Classification A .M.S. : 49 A 22.. Annales de l’Institut Henri Poincaré - Analyse non linéaire - 0294-1449 Vol. 9/92/04/465/ 14I$3.40/ O Gauthier-Villars 466 A. CELLINA AND F. FLORES 1. INTRODUCTION In this paper, we deal with .a class of integrals of the Calculus of Variations without convexity assumptions on their integrands. More preci- sely, we consider problems of the form: where B is the unit ball and À is anon negative number, and we see

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