Let  K = \{ (x,y) | -1<x<1 , -1<y<1 \} . Find the unique soloution of dirichlet problem:

\Delta u(x,y) =0 ,  (x,y) \in K ,
 u(x,y) = |x+y| , (x,y) \in \partial K .
We need to guess a soloution and not use seperation of variables!
Hope you'll be able to help me!
Thanks !