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Math Help - laplace equation

  1. #1
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    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?
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  2. #2
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    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.
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