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On certain minimax problems and Pontryagin’s maximum principle

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Abstract

This paper deals with minimax problems for nonlinear differential expressions involving a vector-valued function of a scalar variable under rather conventional structure conditions on the cost function. It is proved that an absolutely minimizing (i.e. globally and locally minimizing) function is continuously differentiable. A minimizing function is also continuously differentiable, provided a certain extra condition is satisfied. The variational method of V.G. Boltyanskii, developed within optimal control theory, is adapted and used in the proof. The case of higher order derivatives is also considered.

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Authors and Affiliations

  1. Department of Mathematics, Linköping University, 58183, Linköping, Sweden

    Gunnar Aronsson

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  1. Gunnar Aronsson
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Correspondence to Gunnar Aronsson.

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Communicated by L. Ambrosio.

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Aronsson, G. On certain minimax problems and Pontryagin’s maximum principle. Calc. Var. 37, 99–109 (2010). https://doi.org/10.1007/s00526-009-0254-1

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  • DOI: https://doi.org/10.1007/s00526-009-0254-1

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