A Note on Gradient Young Measure Relaxation of Dieudonné-Rashevsky Type Control Problems with Integrands f(s, ξ, v)

We prove a relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type in terms of generalized controls. The main ingredient of the proof is a characterization theorem for gradient Young measures supported on the convex control domain $K\subset \R^{nm}$, which generalizes previous work of Kinderlehrer and Pedregal.