A UNIQUENESS RESULT FOR A NON-STRICTLY CONVEX PROBLEM IN THE CALCULUS OF VARIATIONS

We prove the uniqueness of the solution for a non-strictly convex problem in the Calculus of Variations of the form φ(∇v) − λv. Here, φ is a convex function not differentiable at the origin and λ is a Lipschitz function. To prove this result we show that under fairly general assumptions, the minimizers are globally Lipschitz continuous