# Poisson integral formula for boundary value problem

I have gotten stuck on a boundary value problem which I believe is to be solved using the Poisson Integral Formula. The problem is: $$\nabla^{2}\psi=0, \psi(x,0)=0, |x|>1 ; |\psi(x,y)|<|x|, |x|\leq 1$$

I know how to solve these problems when the values on the boundary are given, as this has a simple formula. However I am unsure now, since I only know it’s bounded between $$-1$$ and $$1$$. This comes up in a class on complex analysis, so I do not believe it will be some advanced PDE technique, I believe the Poisson Integral Formula will be used.

• The conditions don't make sense for $x\in [-1,0].$ – zhw. Mar 10 '19 at 18:09
• @zhw. How come? I copied the question exactly and I do not see why that would cause a problem – Tyler6 Mar 10 '19 at 18:26
• Books can have mistakes. Clearly $|\psi(x,y)|<x, |x|\leq 1$ cannot hold (try $x=-1/2$) – zhw. Mar 10 '19 at 18:39
• @zhw. I edited the question to fix that. Do you know any way to solve it now? – Tyler6 Mar 10 '19 at 19:24