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 = f on ∂B: We distinguish two cases of nonnegative perturbation φ: trivial and nontrivial.
We derive differential relations between the Dunkl spherical and solid means of continuous functions. Next we use the relations to give inductive proofs of mean-value properties for the Dunkl polyharmonic functions and their converses.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.