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.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 77, Complex Analysis and Topology, 2012.
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Abreu-Blaya, R., Bory-Reyes, J. & Kats, B.A. On the solvability of the jump problem in clifford analysis. J Math Sci 189, 1–9 (2013). https://doi.org/10.1007/s10958-013-1171-6
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DOI: https://doi.org/10.1007/s10958-013-1171-6