# [SOLVED]Mean value

#### dwsmith

##### Well-known member
For the Dirichlet problem on a sphere of radius a with the boundary condition
$$u(a,\theta,\phi) = f(\theta,\phi),$$
show that the value of $u$ at the origin $(r = 0)$ is equal to the average value of $f$ over the surface of the sphere.

I know that the max and min occur on the boundaries and that is because the origin is the mean value but I don't know how to show it is the mean value.