  In this article, we introduce higher order conjugate Poisson and Poisson
kernels, which are higher order analogues of the classical conjugate Poisson
and Poisson kernels, as well as the polyharmonic fundamental solutions, and
define multi-layer potentials in terms of Poisson field and the polyharmonic
fundamental solutions, in which the former formed by the higher order conjugate
Poisson and Poisson kernels. Then by the multi-layer potentials, we solve three
classes of boundary value problems (i.e., Dirichlet, Neumann and regularity
problems) with $L^{p}$ boundary data for polyharmonic equations in Lipschitz
domains and give integral representation (or potential) solutions of these
problems.
