Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 21 (2014), No. 2, 453--476Copyright Heldermann Verlag 2014 A Note on Gradient Young Measure Relaxation of Dieudonné-Rashevsky Type Control Problems with Integrands f(s, ξ, v) Marcus Wagner Dept. of Mathematics, University of Leipzig, Postfach 10 09 20, 04009 Leipzig, Germany marcus.wagner@math.uni-leipzig.de [Abstract-pdf] \def\R{\mathbb{R}} We prove a relaxation theorem for multidimensional control problems of Dieudonn\'e-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. Keywords: Multidimensional control problem, minimal value, nonconvex relaxation, lower semicontinuous quasiconvex envelope, gradient Young measure. MSC: 26B25, 26E25, 46G10, 49J20, 49J45 [ Fulltext-pdf  (229  KB)] for subscribers only.