On the solvability of the jump problem in clifford analysis

Abstract:

Let Ω be a bounded open and oriented connected subset of ℝn which has a compact topological boundary Γ, let C be the Dirac operator in ℝn, and let ℝ0,n be the Clifford algebra constructed over the quadratic space ℝn. An ℝ0,n-valued smooth function f: Ω → ℝ0,n in Ω is called monogenic in Ω if Df = 0 in Ω. The aim of this paper is to present the most general condition on Γ obtained so far for which a Hölder continuous function f can be decomposed as F+ - F- = f on Γ, where the components F ± are extendable to monogenic functions in Ω± with Ω+:= Ω, and Ω-:= ℝn \ (Ω ∪ Γ), respectively. © 2013 Springer Science+Business Media New York.

Año de publicación:

2013

Keywords:

Fuente:

scopus