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Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations

Author

Listed:
  • Hongfen Yuan

    (School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China)

  • Valery Karachik

    (Department of Mathematical Analysis, South Ural State University (NRU), 454080 Chelyabinsk, Russia)

Abstract

Dunkl operators are a family of commuting differential–difference operators associated with a finite reflection group. These operators play a key role in the area of harmonic analysis and theory of spherical functions. We study the solution of the inhomogeneous Dunkl polyharmonic equation based on the solutions of Dunkl–Possion equations. Furthermore, we construct the solutions of Dirichlet and Neumann boundary value problems for Dunkl polyharmonic equations without invoking the Green’s function.

Suggested Citation

  • Hongfen Yuan & Valery Karachik, 2023. "Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations," Mathematics, MDPI, vol. 11(9), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2185-:d:1140199
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    References listed on IDEAS

    as
    1. Valery Karachik & Batirkhan Turmetov & Hongfen Yuan, 2022. "Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball," Mathematics, MDPI, vol. 10(7), pages 1-21, April.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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    2. Valery Karachik & Batirkhan Turmetov & Hongfen Yuan, 2022. "Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball," Mathematics, MDPI, vol. 10(7), pages 1-21, April.

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