In this paper we prove the existence of a solution in L∞loc to the Euler-Lagrange equation for the variational problem inf (0.1) with convex closed subset of with non empty interior. We next show that if D* is strictly convex, then the Euler-Lagrange equation can be reduced to an ODE along characteristics, and we deduce that the solution to Euler-Lagrange is different from a.e. and satisfies a uniqueness property. Using these results, we prove a conjecture on the existence of variations on vector fields [6].
On the Euler-Lagrange equation for a variational problem / Bianchini, Stefano. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 17:3(2007), pp. 449-480. [10.3934/dcds.2007.17.449]
On the Euler-Lagrange equation for a variational problem
Bianchini, Stefano
2007-01-01
Abstract
In this paper we prove the existence of a solution in L∞loc to the Euler-Lagrange equation for the variational problem inf (0.1) with convex closed subset of with non empty interior. We next show that if D* is strictly convex, then the Euler-Lagrange equation can be reduced to an ODE along characteristics, and we deduce that the solution to Euler-Lagrange is different from a.e. and satisfies a uniqueness property. Using these results, we prove a conjecture on the existence of variations on vector fields [6].| File | Dimensione | Formato | |
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