Tri-harmonic boundary value problems in a sector

摘要

This paper is devoted to the construction of a tri-harmonic Green function and a tri-harmonic Neumann function in a sector with angle θ = π (n ≥ 1, n ∈ N) explicitly, as well as a tri-harmonic Neumann function in the unit disk. Then the related Dirichlet and Neumann problems for the tri-Poisson equation are discussed, respectively.