📂Functions

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.

See Also

• Harmonic functions
• Biharmonic functions
• Polyharmonic functions