Let $V=L^2(\Omega)$, and $$k=\{v \in V ~s.t ~||v||_{L^2(\Omega)}\leq 1 \}$$ I need to find projection for any $u \in V$ on $k$.
Please help me.I do not have any idea about this problem. I have many theorem about exisitence and uniqueness solution, but I do not know how to find it.
Thanks.