# Thread: Uniqeness of weak solution to variational problem

1. ## Uniqeness of weak solution to variational problem

I have been trying to show that the weak solution $u \in H^1(\Omega)$ such that
$\displaystyle\int_\Omega \nabla u . \nabla v + \alpha + \displaystyle\int_{\partial\Omega} uv = \displaystyle\int_\Omega vf$ for all $v \in H^1(\Omega)$

is unique. I have been told this is hard. I could use Lax-Milgram to show existance and uniqueness but am finding it hard to show coercivity and continuity... any ideas... I only have to show uniqueness, not existence...

2. is it something to do with showing the LHS is an inner product??