We consider a Dirichlet minimum problem with a pointwise constraint on the gradient, i.e., parallel todelu(x)parallel to less than or equal to 1 a.e., or, equivalently, an unconstrained minimum problem with an extended-valued integrand. Since the subdifferential of this integrand is defined on the whole effective domain, the problem of the validity of the Euler Lagrange equation (or, equivalently, of the Pontryagin maximum principle) for a solution w can be posed. T show that this equation is verified along a solution, the equivalence of the problem considered here and of a problem with obstacles is proved, and a generalization of Stampacchia's bounded slope condition result is presented.