TY - JOUR
T1 - On the solvability of the jump problem in clifford analysis
AU - Abreu-Blaya, R.
AU - Bory-Reyes, J.
AU - Kats, B. A.
N1 - Funding Information:
Acknowledgments. The third author was partially supported by the Russian Foundation for Basic Research (project Nos. 09-01-12188-ofi-m and 10-01-00076-a).
PY - 2013/2
Y1 - 2013/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84872190704&partnerID=8YFLogxK
U2 - 10.1007/s10958-013-1171-6
DO - 10.1007/s10958-013-1171-6
M3 - Artículo
SN - 1072-3374
VL - 189
SP - 1
EP - 9
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 1
ER -