We prove the validity of the Euler-Lagrange equation for a so- lution u to the problem of minimizing R ∫,Ω(x, u(x),u(x)) dx, where L is a Carathéodory function, convex in its last variable, without assuming differen-tiability with respect to this variable.
Bonfanti, G., Cellina, A. (2010). The validity of the Euler-Lagrange equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 28(2), 511-517 [10.3934/dcds.2010.28.511].
The validity of the Euler-Lagrange equation
BONFANTI, GIOVANNI;CELLINA, ARRIGO
2010
Abstract
We prove the validity of the Euler-Lagrange equation for a so- lution u to the problem of minimizing R ∫,Ω(x, u(x),u(x)) dx, where L is a Carathéodory function, convex in its last variable, without assuming differen-tiability with respect to this variable.
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