The validity of the Euler-Lagrange equation for solutions to variational functionals with fast growth
Agnese Caielli, Arrigo Cellina · LIBERTAS MATHEMATICA (new series) · 2013
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 differentiability on L.