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

2014/02/07 by Mohamed Ben Chrouda, Chrouda, Mohamed Ben, Khalifa El Mabrouk +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1402.1597

openalex publication_date 2014/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Combining probabilistic and analytic tools from potential theory, we investigate Dirichlet problems associated with the Dunkl Laplacian Δ_k. We establish, under some conditions on the open set D⊂\R^d, the existence of a unique continuous function h in the closure of D, twice differentiable in D, such that Δ_kh=0 \textrmin D \textrmand h=f \textrmon ∂ D. We also give a probabilistic formula characterizing the solution h. The function f is assumed to be continuous on the Euclidean boundary ∂ D of D.

Citations

• Mean value property associated with the Dunkl Laplacian

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