Solution
= Solution
The <Lax-Milgram theorem> states that if $H$ is a real <Hilbert space>, $B:H\times H\to\mathbb R$ is a <bounded bilinear form>, and there is an $\alpha>0$ such that
$$
B(v,v)\geq\alpha\|v\|_H^2
\qquad(v\in H),
$$
then for every bounded linear functional $F\in H'$ there is a unique $u\in H$ satisfying
$$
B(u,v)=F(v)
\qquad(v\in H).
$$
Moreover, $\boxed{\|u\|_H\leq\alpha^{-1}\|F\|_{H'}}$. Symmetry of $B$ is not required.