# Math Help - laplace equation

1. ## laplace equation

$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0, u=-K \quad\mbox{at} \quad x=\pm b, y=\pm h$

How to solve this?

2. If you let $u = v - K$ then $v$ satisfies

$\dfrac{\partial^2 v}{\partial x^2} + \dfrac{\partial^2 v}{\partial y^2} = 0$

where $v = 0$ on the boundary of the rectangle. The solution of this second problem is $v \equiv 0$. Thus, the solution of your problem us $u = -K$ on the entire region.