Riemann Boundary Value Problem for Triharmonic Equation in Higher Space

We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: Δ(3)[u](x) = 0, x ∈ R ( n )∖∂Ω, u (+)(x) = u (−)(x)G(x) + g(x), x ∈ ∂Ω, (D ( j ) u)(+)(x) = (D ( j ) u)(−)(x)A ( j ) + f ( j )(x), x ∈ ∂Ω, u(∞) = 0, where (j = 1,…, 5) ∂Ω is a Lyapunov surface in R ( n ), D = ∑( k=1) ( n ) e ( k )(∂/∂x ( k )) is the Dirac operator, and u(x) = ∑( A ) e ( A ) u ( A )(x) are unknown functions with values in a universal Clifford algebra Cl(V ( n,n )). Under some hypotheses, it is proved that the boundary value problem has a unique solution.