6.2: Harmonic Functions
( \newcommand{\kernel}{\mathrm{null}\,}\)
We start by defining harmonic functions and looking at some of their properties.
A function u(x,y) is called harmonic if it is twice continuously differentiable and satisfies the following partial differential equation:
∇2u=uxx+uyy=0.
Equation ??? is called Laplace’s equation. So a function is harmonic if it satisfies Laplace’s equation. The operator ∇2 is called the Laplacian and ∇2u is called the Laplacian of u.