I would recommend defining U(x,y,z)= (w/2-|x-w/2|)(h/2-|y-h/2|)z and define [tex]W(x,y,z)= V(x,y,z)- U(x,y,z)[/itex] then W will be 0 on all surfaces. .

You should be able to find (treat -w/2< x< 0, 0< x< w/2, -h/2< y< 0, and 0< y< h/2 separately) and then apply "separation of variables" to solving for W(x,y,z).