Boundary value problems for the Dunkl Laplacian

Abstrakt

Let Δ_k be the Dunkl Laplacian on ℜ^d associated with a reflection group W and a multiplicity function k. The purpose of this paper is to establish the existence and the uniqueness of a positive solution on the unit ball B of ℜ^d to the following boundary value problem:

Δ_ku = φu in B and u = ƒ on ∂B

We distinguish two cases of nonnegative perturbation φ: trivial and nontrivial.