Higher-Order Noether’s Theorem for Isoperimetric Variational Problems

Gastão Frederico (), Matheus Jatkoske Lazo (), Maria Nilde Barreto () and José Vanterler da Costa Sousa ()
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Gastão Frederico: Federal University of Ceará
Matheus Jatkoske Lazo: Federal University of Rio Grande
Maria Nilde Barreto: Federal University of Ceará
José Vanterler da Costa Sousa: Federal University of ABC

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 2, No 5, 568 pages

Abstract: 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.

Keywords: Higher-order Noether’s theorem; Variational isoperimetric problems; DuBois-Reymond conditions; Euler–Lagrange equations; 49S05; 70H03; 49K15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02288-z

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