Abstract

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⊂RnmK\subset \R^{nm}, which generalizes previous work of Kinderlehrer and Pedregal.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Multidimensional control problem
  • minimal value
  • nonconvex relaxation
  • lower semicontinuous quasiconvex envelope
  • gradient Young measure

Mathematics Subject Classification

26B25, 26E25, 46G10, 49J20, 49J45

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Suggested citation

M. Wagner. “A Note on Gradient Young Measure Relaxation of Dieudonné-Rashevsky Type Control Problems with Integrands f(s, ξ, v).” Journal of Convex Analysis 21 (2014), No. 2, 453–476. https://doi.org/10.68381/jca21024

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.