Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains

We investigate the boundary trace operators that naturally correspond to $H(\mathrm{curl},\Omega )$, namely the tangential and twisted tangential trace, where $\Omega \subseteq R^3$. In particular we regard partial tangential traces, i.e., we look only on a subset Γ of the boundary ∂Ω. We assume both Ω and Γ to be strongly Lipschitz (possibly unbounded). We define the space of all $H(\mathrm{curl},\Omega )$ fields that possess a $L^2$ tangential trace in a weak sense and show that the set of all smooth fields is dense in that space, which is a generalization of [1]. This is especially important for Maxwell's equation with mixed boundary condition as we answer the open problem by Weiss and Staffans in [10, Sec. 5] for strongly Lipschitz pairs.