Polyharmonic Functions
Definition
Let $\Delta = \nabla^{2}$ be called a Laplacian. For a natural number $k \in \mathbb{N}$, $\Delta ^{k}$ is referred to as a polyharmonic operator or a polylaplacian. The equation below is called the polyharmonic equation.
$$ \Delta^{k} f = 0 $$
The solutions to the polyharmonic equation are referred to as polyharmonic functions.
Description
It is a generalization of harmonic functions.