We prove higher integrability properties of solutions to the problem of minimizing ∫ σ L(x, u(x),δu(x))dx, where X → L(x, u, X) 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 exponentia
Bonfanti, G., Cellina, A., Mazzola, M. (2012). The higher integrability and the validity of the Euler-Lagrange equation for solutions to variational problems. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 50(2), 888-899 [10.1137/110820890].
The higher integrability and the validity of the Euler-Lagrange equation for solutions to variational problems
BONFANTI, GIOVANNI
;CELLINA, ARRIGO
;MAZZOLA, MARCO
2012
Abstract
We prove higher integrability properties of solutions to the problem of minimizing ∫ σ L(x, u(x),δu(x))dx, where X → L(x, u, X) 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 exponentia
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