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On certain minimax problems and Pontryagin’s maximum principle
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2010 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 37, no 1-2, 99-109 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer , 2010. Vol. 37, no 1-2, 99-109 p.
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URN: urn:nbn:se:liu:diva-67329DOI: 10.1007/s00526-009-0254-1OAI: diva2:409367
Available from: 2011-04-08 Created: 2011-04-08

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Aronsson, Gunnar
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Applied MathematicsThe Institute of Technology
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