On the Dirichlet problem associated with Dunkl Laplacian

Abstract

This paper is devoted to the study of the Dirichlet problem associated with the Dunkl Laplacian ${\Delta }_k$. We establish, under some condition on a bounded domain $D$ of ${\mathbb{R}}^d$, the existence of a unique continuous function $h$ on ${\mathbb{R}}^d$ such that ${\Delta }_{k}h=0$ on $D$ and $h=f$ on ${\mathbb{R}}^d\setminus D$ the complement of $D$ in ${\mathbb{R}}^d$, where the function $f$ is asumed to be continuous. We also give an analytic formula characterizing the solution $h$.

6 pages

References in corpus (1)

• Dirichlet problem associated with Dunkl Laplacian on $W$-invariant open sets