The biharmonic principal
function problem is the construction of a biharmonic function in a space which
“imitates” the behavior of a given singularity function. In this paper we first define
the notion of a biharmonic operator which clarifies the modes of “imitation.”
We then prove the existence and uniqueness theorem of the biharmonic
principal function. The theory is a generalization of the harmonic principal
functions to the larger family of biharmonic functions. An indication of its
application as well as its further generalization to polyharmonic functions is also
given.
