Polyharmonic function

Summary

A polyharmonic function of order $m$ is a function whose $m$-fold iterated Laplacian vanishes: $\Delta^m u = 0$. For $m = 1$ these are the harmonic functions, and for $m = 2$ the solutions of the biharmonic equation. Polyharmonic functions are the model solutions of higher-order elliptic equations. They appear in elasticity and in the study of polyharmonic splines and interpolation.