polyharmonic functions

Polyharmonic functions are mathematical functions that generalize harmonic functions. They satisfy a differential equation where applying the Laplacian operator (a measure of how a function curves) multiple times results in zero. For example, a biharmonic function becomes harmonic after applying the Laplacian twice. These functions often appear in physics and engineering, particularly in elasticity and fluid flow, where they model systems with equilibrium states or smooth distributions. Essentially, polyharmonic functions ensure a balance or smoothness over a domain, extending the idea of harmonic functions to more complex, higher-order scenarios.