Journal of Convex Analysis 07 (2000), No. 1, 167--182
Copyright Heldermann Verlag 2000
Euler-Lagrange Inclusions and Existence of Minimizers for a Class of Non-Coercive Variational Problems
Dip. di Matematica Pura ed Applicata, UniversitÓ di Modena, 41100 Modena, Italy
Dip. di Matematica, UniversitÓ di Roma 1, Piazzale A. Moro 2, 00185 Roma, Italy
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.
Keywords: Calculus of variations, existence, Euler-Lagrange inclusions, radially symmetric solutions, non-coercive problems.
MSC: 49J10, 45K05; 49J30
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