Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations

Hongfen Yuan () and Valery Karachik
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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

Mathematics, 2023, vol. 11, issue 9, 1-15

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.

Keywords: neumann problem; dirichlet problem; dunkl polyharmonic equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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