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On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball

Author

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  • Valery Karachik

    (Department of Mathematical Analysis and Methods of Teaching Mathematics, South Ural State University, 454080 Chelyabinsk, Russia)

Abstract

In this paper, based on a new representation of the Green’s function of the Navier problem for the 3-harmonic equation in the unit ball, an integral representation of the solution of the corresponding Navier problem is found. Then, for the Navier problem for a homogeneous 3-harmonic equation, the obtained representation of the solution is reduced to a form that does not explicitly contain the Green’s function.

Suggested Citation

  • Valery Karachik, 2025. "On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball," Mathematics, MDPI, vol. 13(10), pages 1-31, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1630-:d:1656733
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    References listed on IDEAS

    as
    1. Valery Karachik, 2021. "Dirichlet and Neumann Boundary Value Problems for the Polyharmonic Equation in the Unit Ball," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    2. M. Akel & H. Begehr, 2017. "Neumann function for a hyperbolic strip and a class of related plane domains," Mathematische Nachrichten, Wiley Blackwell, vol. 290(4), pages 490-506, March.
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