Let $\displaystyle V=L^2(\Omega)$ and for $\displaystyle r>0$:

$\displaystyle K=\{v\in V : ||v||_{L^2(\Omega)}\leq r\}$.

For any $\displaystyle u\in V$, find its projection on $\displaystyle K$.

I have no idea where to start. I know that the projection map has certain properties (linear, self-adjoint, operator norm of 1, whatever), but is there any specific formula to find it?