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



Density of $H^{1/2}(\partial \Omega)$ in $L_2(\partial\Omega)$
Lipschitz continuous functions on $\Gamma$ are dense in $L^2(\Gamma)$ and are contained in $H^{1/2}(\Gamma)$.


