On the Euler-Lagrange equation for functionals of the calculus of variations without upper growth conditions. (English) Zbl 1201.49022

Degiovanni, Marco; Marzocchi, Marco

SIAM J. Control Optim. 48, No. 4, 2857-2870 (2009).

Summary: 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 assumed to be convex, but no upper growth condition is imposed.

MSC:

49K20	Optimality conditions for problems involving partial differential equations
35J20	Variational methods for second-order elliptic equations

Keywords:

calculus of variations; elliptic equations; minima; Euler-Lagrange equations