Dirichlet type problems for Dunkl-Poisson equations

Boundary value problems

Hongfen Yuan¹ 

[1] College of Science, Hebei University of Engineering, Handan, P.R. China

关键词: Dirichlet problem;    Dunkl-Poisson equation;    Dunkl-Laplace equation;    Clifford analysis;    30G35;    35J05;    58C50;   

DOI  :  10.1186/s13661-016-0730-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, using the intertwine relations of differential operators, we study one representation of real analytic functions by Dunkl-harmonic functions, which is a generalization of the well-known Almansi formula. As an application of the representation, we construct a solution of the Dunkl-Poisson equations in Clifford analysis. Then we investigate solutions of homogeneous and inhomogeneous Dirichlet type problems for Dunkl-Poisson’s equation, and inhomogeneous Dirichlet problems for Dunkl-Laplace’s equation.

【 授权许可】

CC BY