Necessary conditions and non-existence results for autonomous nonconvex variational problems |
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| Authors: | Giovanni Cupini Marcello Guidorzi Cristina Marcelli |
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| Affiliation: | aDipartimento di Matematica “U. Dini” – Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy;bDipartimento di Scienze Matematiche – Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy |
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| Abstract: | Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained. |
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| Keywords: | Autonomous variational problem Necessary condition DuBois-Reymond condition Non-existence result Subdifferential Maximum principle |
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