The validity of the Euler-Lagrange equation for solutions to variational functionals with fast growth

Abstract

For L convex and defined on R^{N}, we consider a solution u to the problem of minimizing ∫_{Ω}L(∇v(x))dx. We provide a growth condition on L to guarantee that u is locally bounded and, by building suitable variations, we prove the validity of the Euler-Lagrange equation without imposing further regularity on L.