A sufficient condition is presented for a simple problem in the calculus of variations. This condition is derived by comparing the functional to be minimized to another functional such that a zero of this is a minimizing element of the former functional. The procedure which results from the sufficient condition to solve the variational problem is specially suited for integrands which do not have some partial derivatives at some points of their domain of definition. Several examples are given which illustrate the range of applicability of the method.