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Izvestiya: Mathematics, 2017, Volume 81, Issue 5, Pages 973–984
DOI: https://doi.org/10.1070/IM8622 (Mi im8622) 		 
An analogue of Pontryagin's maximum principle in problems of minimization of multiple integrals

M. I. Zelikinab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (287 kB) Russian version article
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DOI: https://doi.org/10.1070/IM8622
Abstract: We prove a theorem on necessary conditions of Pontryagin's maximum principle type for an optimum of functionals given by multiple integrals. In contrast to the case of one-dimensional integrals, the maximum of the Pontryagin function is taken only over matrices of rank 1, not over all matrices. We give some examples.
Keywords: Pontryagin's maximum principle, multiple integrals, transversality conditions, necessary and sufficient conditions for strong or weak minima, semicontinuous extensions of variational problems, fields of extremals.
Received: 26.10.2016
Revised: 27.01.2017
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 49K20, 49Q20, 58E15, 70H05
Language: English
Original paper language: Russian
Citation: M. I. Zelikin, “An analogue of Pontryagin's maximum principle in problems of minimization of multiple integrals”, Izv. Math., 81:5 (2017), 973–984
Citation in format AMSBIB
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\paper An analogue of Pontryagin's maximum principle in problems of minimization of multiple integrals
\jour Izv. Math.
\yr 2017
\vol 81
\issue 5
\pages 973--984
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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