We consider the following classical autonomous variational problem minimize F (v) =\int_a^b f (v(x), v (x)) dx : v ∈ AC([a, b]), v(a) = α, v(b) = β , where the Lagrangian f is possibly neither continuous, nor convex, nor coercive. We prove a monotonicity property of the minimizers stating that they satisfy the maximum principle or the minimum one. By virtue of such a property, applying recent results concerning constrained variational prob- lems, we derive a relaxation theorem, the DuBois-Reymond necessary condition and some existence or non-existence criteria.

Monotonicity properties of minimizers and relaxation for autonomous variational problems / G. Cupini; C. Marcelli. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 17:(2011), pp. 222-242. [10.1051/cocv/2010001]

Monotonicity properties of minimizers and relaxation for autonomous variational problems

CUPINI, GIOVANNI;
2011

Abstract

We consider the following classical autonomous variational problem minimize F (v) =\int_a^b f (v(x), v (x)) dx : v ∈ AC([a, b]), v(a) = α, v(b) = β , where the Lagrangian f is possibly neither continuous, nor convex, nor coercive. We prove a monotonicity property of the minimizers stating that they satisfy the maximum principle or the minimum one. By virtue of such a property, applying recent results concerning constrained variational prob- lems, we derive a relaxation theorem, the DuBois-Reymond necessary condition and some existence or non-existence criteria.
2011
Monotonicity properties of minimizers and relaxation for autonomous variational problems / G. Cupini; C. Marcelli. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 17:(2011), pp. 222-242. [10.1051/cocv/2010001]
G. Cupini; C. Marcelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/79079
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