let $\Omega$ be a bounded domain of $\mathbf{R}^n$ with a smooth boundary $\Gamma$.
$u_n:\Omega\times[0,T]\rightarrow \mathbf{R}$
$ a\left(.,.\right):H^1_0\left(\mathbf{R}\right)\times H^1_0\left(\mathbf{R}\right)\rightarrow \mathbf{R}$ a form which is bilinear,symmetric and continous.
if $ u_n\rightarrow u$ weakly star in$ L^{\infty}\left([0,T];H^1_0\left(\Omega\right)\right).$
How can we show that:
$a \left(u_n,v\right) \rightarrow a \left(u,v\right)$weakly star in $L^{\infty}\left([0,T]\right) \forall v\in H^1_0\left(\Omega\right)$