# The Higher Integrability and the Validity of the Euler-Lagrange Equation for Solutions to Variational Problems

1 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : We prove higher integrability properties of solutions to the problem of minimizing $\int_{\Omega}L(x,u(x),\nabla u(x))\rm{ d}x,$ where $\xi\mapsto L(x,u,\xi)$ is a convex function satisfying some additional conditions. As an application, we prove the validity of the Euler-Lagrange equation for a class of functionals with growth faster than exponential.
Type de document :
Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (2), pp.888-899. 〈10.1137/110820890〉

https://hal.inria.fr/hal-00724827
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 17:28:52
Dernière modification le : vendredi 7 décembre 2018 - 01:23:08

### Citation

Giovanni Bonfanti, Arrigo Cellina, Marco Mazzola. The Higher Integrability and the Validity of the Euler-Lagrange Equation for Solutions to Variational Problems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (2), pp.888-899. 〈10.1137/110820890〉. 〈hal-00724827〉

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