Riemann boundary value problem for harmonic functions in Clifford analysis - Longfei, Gu; Zhongxiang, Zhang (Mathematische Nachrichten, 2014)
In this article, we mainly deal with the boundary value problem for harmonic function with values in Clifford algebra: Δ[u](x)=0,x∈Rn∖∂Ω,u+(x)=u−(x)G(x)+g1(x),x∈∂Ω,(Du)+(x)=(Du)−(x)A+g2(x),x∈∂Ω,∥u(∞)∥=0,where ∂Ω is a Liapunov surface in Rn, the Dirac operator D=∑k=1nek∂∂xk, u(x)=∑AeAuA(x) are unknown functions with values in a universal Clifford algebra Cl(Vn,n). Under some assumptions, we show that the boundary value problem is solvable.