I try to solve
$$\Delta^2u=f$$ on unit square. with $f=4\sin(\pi x)\sin(\pi y)$
Using $v=-\Delta u,$ leads to $$v+\Delta u=0,$$ $$-\Delta v=f.$$
By Dirichlet boundary condition on $u$.
What is the another boundary condition? Could I use Dirichlet boundary condition for $v$?When I use this condition the answer is true. Otherwise it is false.
How could I determine the boundary condition. Is there any refrence to help me about that?
Please help me.Thanks a lot.