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

$\displaystyle \Delta u(x,y) =0 $ , $\displaystyle (x,y) \in K $ ,
$\displaystyle u(x,y) = |x+y| $ , $\displaystyle (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 !