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

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

Mathematics, 2025, vol. 13, issue 10, 1-31

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.

Keywords: 3-harmonic equation; biharmonic equation; Navier problem; Green’s function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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