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Kods Hassine

Publications and source records attributed to Kods Hassine.

3 recordsLinked to original sources
arXiv2015

Potential theory associated with the Dunkl Laplacian

The main goal of this paper is to give potential theoretical approach to study the Dunkl Laplacian $Δ_k$ which is a standard example of differential-difference operators. By introducing the Green kernel relative to $Δ_k$, we prove that the Dunkl Laplacian generates a balayage space and we investigate the associated family of harmonic measures. Therefore, by mean of harmonic kernels, we give a characterization of all $Δ_k$-harmonic functions on large class of open subsets $U$ of $\mathbb{R}^d$. We also establish existence and uniqueness result of a solution of the corresponding Dirichlet problem.

math.CA↗
arXiv2015

Semilinear equations associated with Dunkl Laplacian

Let $Δ_k$ be the Dunkl Laplacian on $\mathbb R^d$ associated with a reflection group $W$ and a multiplicity function $k$. The purpose of this paper is to establish necessary and sufficient condition under which there exists a positive solution of the equation $Δ_ku=φ(u)$ in the unit ball of $\mathbb R^d$ as well as in the whole space $\mathbb R^d$.

math.AP↗