Hi,

i know that the following statement is used extensively, but i cannot find a proof anywhere:

For $\Omega$ a Lipschitz domain with boundary $\Gamma$, the space $H^{1/2}(\Gamma)$ is dense in $L_2(\Gamma)$.

Here, the space $H^{1/2}(\Gamma)$ is defined as the trace space, i.e. as $\gamma_0(H^1(\Omega))$, where $\gamma_0$ is the trace operator.

I read that one has to use density of $C^\infty(\overline\Omega)$ in $H^1(\Omega)$, but i dont see how - i can't extend an $L_2(\Gamma)$ function to a function in $H^1(\Omega)$ in a bounded way, right?

I tried Google and looked in all the books I have access to, but didn't find a proof. Does anyone have a hint?

Thanks, Mike