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Journal Articles SIAM Journal on Control and Optimization Year : 2012

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

Giovanni Bonfanti
  • Function : Author
Arrigo Cellina
  • Function : Author

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.

Dates and versions

hal-00724827 , version 1 (22-08-2012)

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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, 2012, 50 (2), pp.888-899. ⟨10.1137/110820890⟩. ⟨hal-00724827⟩
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