On Integral Representation Formulae for Biharmonic Functions on the Ball

Biharmonic functions are solutions of the fourth order partial differential equation ΔΔu = 0. A simple method is proposed for deriving integral representation formulae for these functions u on the n‐dimensional ball. Poisson‐type representations in the setting of Hardy Spaces are obtained for biharmonic functions subject to Dirichlet, Riquier and other boundary conditions. The approach exploits algebraic properties of a first order partial differential operator and its resolvent.