Geodesic
Euler-Lagrange Inclusions and Existence of Minimizers for a Class of Non-Coercive Variational Problems
Journal of convex analysis, Tome 7 (2000) no. 1, pp. 167-182
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We prove the existence of radially symmetric minimizers, in the class of Sobolev vector-valued functions vanishing on the boundary of a ball, for convex non-coercive integral functionals. We associate to the functional a system of differential inclusions of Euler-Lagrange type, and we prove that the solvability of these inclusions is a necessary and sufficient condition for the existence of a radially symmetric minimizer.
Classification : 49J10, 45K05, 49J30
Mots-clés : Calculus of variations, existence, Euler-Lagrange inclusions, radially symmetric solutions, non-coercive problems 
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     author = {G. Crasta and A. Malusa},
     title = {Euler-Lagrange {Inclusions} and {Existence} of {Minimizers} for a {Class} of {Non-Coercive} {Variational} {Problems}},
     journal = {Journal of convex analysis},
     pages = {167--182},
     year = {2000},
     volume = {7},
     number = {1},
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G. Crasta; A. Malusa. Euler-Lagrange Inclusions and Existence of Minimizers for a Class of Non-Coercive Variational Problems. Journal of convex analysis, Tome 7 (2000) no. 1, pp. 167-182. http://geodesic.mathdoc.fr/item/JCA_2000_7_1_JCA_2000_7_1_a7/