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Journal of Convex Analysis 21 (2014), No. 2, 453--476
Copyright 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


\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

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