Mean Value Property

$f(x,y)\text{ is harmonic}\to \forall (x,y)\in \mathcal{D},f(x,y)=\frac{1}{\text{perimeter}}{\oint }_{\partial \mathcal{D}}f(x,y)ds$

• Essentially states that if a function is harmonic, all of its point on the surface satisfy the property that $f(x,y)$ is the same as the average along the circumference of a circle surrounding $(x,y)$