0

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 $L^{\infty}\left([0,T]\right) \forall v\in H^1_0\left(\Omega\right)$

sd19
  • 19
  • Are you asking for an example? Or you’re asking how to show whether a sequence converge weak-star in $L^\infty$? – Jack LeGrüß Oct 08 '20 at 21:41
  • I am asking how to show $a \left(u_n,v\right) \rightarrow a \left(u,v\right)$weakly star in $L^{\infty}\left([0,T]\right) \forall v\in H^1_0\left(\Omega\right)$ – sd19 Oct 08 '20 at 21:50

0 Answers0