For a class of functionals of the Calculus of variations, we prove that each minimum of the functional satisfies the associated Euler-Lagrange equation. The integrand is supposed to be convex, but no upper growth condition is imposed.
Degiovanni, M., Marzocchi, M., On the Euler-Lagrange equation for functionals of the calculus of variations without upper growth conditions, <<SIAM JOURNAL ON CONTROL AND OPTIMIZATION>>, 2009; 48 (4): 2857-2870. [doi:10.1137/090747968] [http://hdl.handle.net/10807/3484]
On the Euler-Lagrange equation for functionals of the calculus of variations without upper growth conditions
Degiovanni, Marco;Marzocchi, Marco
2009
Abstract
For a class of functionals of the Calculus of variations, we prove that each minimum of the functional satisfies the associated Euler-Lagrange equation. The integrand is supposed to be convex, but no upper growth condition is imposed.
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