mean value property

A partial differential equation $$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$$ is defined for the two-dimensional field $T: T(x, y)$, inside a planar...

The function $f(x, y)$ satisfies the Laplace equation $\nabla^2 f(x, y) = 0$ on a circular domain of radius $r = 1$ with its center at point $P$ with coordinates $x = 0, y = 0$. Th...