Potential theory associated with the Dunkl Laplacian

Hassine, Kods

doi:10.1515/apam-2015-0056

Cited by 1 publication

(2 citation statements)

References 19 publications

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“…is infinitely differentiable on D. We note that the problem of the hypoellipticity of ∆ k is discussed in [5,6] We also choose the ball B small enough such that, for every α ∈ R + , It is clear that the function g 2 is not trivial and Nh = g 1 + g 2 . Now, assume that h ∈ C ∞ (D).…”

Section: Resultsmentioning

confidence: 99%

“…We derive from this formula that, for every x ∈ D, H ∆ k D f (x) depends only on the values of f on ∪ α∈R + σ α (D) and on ∂D the Euclidean boundary of D. If, in addition, we assume that f is locally Hölder continuous on ∪ α∈R + σ(D) then H ∆ k D f is continuously twice differentiable on D and therefore the first equation in (1) is fulfilled by H ∆ k D f not only in the sense of distributions but also pointwise. It was shown in [5,6]…”

Section: Introductionmentioning

confidence: 93%

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On the Dirichlet problem associated with the Dunkl Laplacian

Chrouda¹

2016

Ann. Polon. Math.

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This paper is devoted to the study of the Dirichlet problem associated with the Dunkl Laplacian ∆ k . We establish, under some condition on a bounded domain D of R d , the existence of a unique continuous function h on R d such that ∆ k h = 0 on D and h = f on R d \ D the complement of D in R d , where the function f is asumed to be continuous. We also give an analytic formula characterizing the solution h.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%