Abstract
The study of the main boundary value problems for complex partial differential equations of any order is limited to model equations. Four main boundary value problems are investigated on the unit disk, namely the Schwarz, Dirichlet, Neumann, Robin problems for analytical functions and more generally for the inhomogeneous Cauchy-Riemann equation. The article considers and proves the properties of Dirichlet and Neumann boundary value problems for three-harmonic functions in a unit disc. The representation of solutions and the conditions of solvability are given explicitly. The fundamental tools are the Gauss theorem and the Cauchy-Pompey representation, as well as Dirichlet and Neumann problems for bi-harmonic equations on a unit circle.