We investigate the minima of functionals of the form ∫ [a,b]g(&udot;(s))ds where g is strictly convex. The admissible functions u : [a,b] → ℝ are not necessarily convex and satisfy u ≤ f on [a,b], u(a) = f(a), u(b) = f(b), f is a fixed function on [a,b]. We show that the minimum is attained by &fmacr;, the convex envelope of f.
