## Dirichlet Problem-Partial Differential Equations

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 !