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Non-Coercive Radially Symmetric Variational Problems: Existence, Symmetry and Convexity of Minimizers

Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, P.le A. Moro 5, 00185 Roma, Italy
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Symmetry 2019, 11(5), 688; https://doi.org/10.3390/sym11050688
Received: 23 April 2019 / Revised: 13 May 2019 / Accepted: 14 May 2019 / Published: 18 May 2019
(This article belongs to the Special Issue Symmetry in Calculus of Variations and Control Theory)
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Abstract

We prove the existence of radially symmetric solutions and the validity of Euler–Lagrange necessary conditions for a class of variational problems with slow growth. The results are obtained through the construction of suitable superlinear perturbations of the functional having the same minimizers of the original one.
Keywords: variational problems; radially symmetric minimizers; Euler–Lagrange inclusions variational problems; radially symmetric minimizers; Euler–Lagrange inclusions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Crasta, G.; Malusa, A. Non-Coercive Radially Symmetric Variational Problems: Existence, Symmetry and Convexity of Minimizers. Symmetry 2019, 11, 688.

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