June  2010, 28(2): 511-517. doi: 10.3934/dcds.2010.28.511

The validity of the Euler-Lagrange equation

1. 

Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via R. Cozzi 53, I-20125 Milano, Italy, Italy

Received  December 2009 Revised  February 2010 Published  April 2010

We prove the validity of the Euler-Lagrange equationfor a solution $u$ to the problem of minimizing $\int_{\Omega}L(x,u(x),\nabla u(x))dx$,where $L$ is a Carathéodory function, convex in its last variable,without assuming differentiability with respect to this variable.
Citation: Giovanni Bonfanti, Arrigo Cellina. The validity of the Euler-Lagrange equation. Discrete & Continuous Dynamical Systems, 2010, 28 (2) : 511-517. doi: 10.3934/dcds.2010.28.511
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