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Higher-Order Noether’s Theorem for Isoperimetric Variational Problems

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Abstract

In this present paper, we concern a non-smooth higher-order extension of Noether’s symmetry theorem for variational isoperimetric problems with delayed arguments. The result is proven to be valid in the class of Lipschitz functions, as long as the delayed higher-order Euler–Lagrange extremals are restricted to those that satisfy the delayed higher-order DuBois-Reymond necessary optimality condition. The important case of delayed isoperimetric optimal control problems is considered as well.

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Acknowledgements

The authors are very grateful to the anonymous reviewers for their useful comments that led to improvement of the manuscript.

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Authors and Affiliations

  1. Federal University of Ceará, Campus de Russas, Russas, Brazil

    Gastão Frederico & Maria Nilde Barreto

  2. Department of Science and Technology, University of Cape Verde, Praia, Santiago, Cape Verde

    Gastão Frederico

  3. Institute of Mathematics, Statistics and Physics, Federal University of Rio Grande, Rio Grande, RS, Brazil

    Matheus Jatkoske Lazo

  4. Center for Mathematics Computing and Cognition, Federal University of ABC, Santo Andre, SP, Brazil

    José Vanterler da Costa Sousa

Authors
  1. Gastão Frederico
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  2. Matheus Jatkoske Lazo
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  3. Maria Nilde Barreto
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  4. José Vanterler da Costa Sousa
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Correspondence to José Vanterler da Costa Sousa.

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Communicated by Nikolai Osmolovskii.

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Frederico, G., Lazo, M.J., Barreto, M.N. et al. Higher-Order Noether’s Theorem for Isoperimetric Variational Problems. J Optim Theory Appl 199, 541–568 (2023). https://doi.org/10.1007/s10957-023-02288-z

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