Boundary value problems for the Dunkl Laplacian

  1. Mohamed Ben Chrouda
  2. Khalifa El Mabrouk
  3. Kods Hassine

Abstract

Let Δk be the Dunkl Laplacian on ℜd 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 ℜd to the following boundary value problem:

Δku = φ(u) in B and u = ƒ on ∂B

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

 

 

 

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Probability and Mathematical Statistics

38, z. 2, 2018

Pages from 249 to 269

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