Mean Value Property

#Math

$\displaystyle f(x,y)\text{ is harmonic}\rightarrow\forall(x,y)\in \mathscr{D},f(x,y)=\frac{1}{\text{perimeter}}\oint_{\partial \mathscr{D}}f(x,y)\space ds$

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