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Recent Advances of Constrained Variational Problems Involving Second-Order Partial Derivatives: A Review

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
    Fundamental Sciences Applied in Engineering—Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania)

Abstract

This paper comprehensively reviews the nonlinear dynamics given by some classes of constrained control problems which involve second-order partial derivatives. Specifically, necessary optimality conditions are formulated and proved for the considered variational control problems governed by integral functionals. In addition, the well-posedness and the associated variational inequalities are considered in the present review paper.

Suggested Citation

  • Savin Treanţă, 2022. "Recent Advances of Constrained Variational Problems Involving Second-Order Partial Derivatives: A Review," Mathematics, MDPI, vol. 10(15), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2599-:d:871819
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    References listed on IDEAS

    as
    1. Savin Treanţă & Muhammad Bilal Khan & Tareq Saeed, 2022. "Optimality for Control Problem with PDEs of Second-Order as Constraints," Mathematics, MDPI, vol. 10(6), pages 1-7, March.
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    Cited by:

    1. Savin Treanţă, 2022. "Variational Problems and Applications," Mathematics, MDPI, vol. 11(1), pages 1-4, December.
    2. Tuan Anh Bui & Jun-Sik Kim & Junyoung Park, 2023. "Efficient Method for Derivatives of Nonlinear Stiffness Matrix," Mathematics, MDPI, vol. 11(7), pages 1-20, March.

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