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Volume 12
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10.3390/axioms12060543
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Article

On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball

by
Valery Karachik
Department of Mathematical Analysis and Methods of Teaching Mathematics, South Ural State University, 454080 Chelyabinsk, Russia
Axioms 2023, 12(6), 543; https://doi.org/10.3390/axioms12060543
Submission received: 23 April 2023 / Revised: 27 May 2023 / Accepted: 29 May 2023 / Published: 31 May 2023
Versions Notes

Abstract

The paper gives an explicit representation of the Green’s function of the Dirichlet boundary value problem for the polyharmonic equation in the unit ball. The solution of the homogeneous Dirichlet problem is found. An example of solving the homogeneous Dirichlet problem with the simplest polynomial right-hand side of the polyharmonic equation is given.
Keywords: Dirichlet problem; polyharmonic equation; Green’s function Dirichlet problem; polyharmonic equation; Green’s function

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MDPI and ACS Style

Karachik, V. On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball. Axioms 2023, 12, 543. https://doi.org/10.3390/axioms12060543

AMA Style

Karachik V. On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball. Axioms. 2023; 12(6):543. https://doi.org/10.3390/axioms12060543

Chicago/Turabian Style

Karachik, Valery. 2023. "On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball" Axioms 12, no. 6: 543. https://doi.org/10.3390/axioms12060543

APA Style

Karachik, V. (2023). On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball. Axioms, 12(6), 543. https://doi.org/10.3390/axioms12060543

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