Riemann Boundary Value Problem for Triharmonic Equation in Higher Space - Longfei Gu (The Scientific World Journal, 2014)
We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: Δ3[u](x)=0, x∈Rn∖∂Ω, u+(x)=u-(x)G(x)+g(x), x∈∂Ω, (Dju)+(x)=(Dju)-(x)Aj+fj(x), x∈∂Ω, u(∞)=0, where (j=1,…,5)  ∂Ω is a Lyapunov surface in Rn, D=∑k=1nek(∂/∂xk) is the Dirac operator, and u(x)=∑AeAuA(x) are unknown functions with values in a universal Clifford algebra Cl(Vn,n). Under some hypotheses, it is proved that the boundary value problem has a unique solution.