Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains
Nathanael Skrepek, Dirk Pauly · Journal of Mathematical Analysis and Applications · 2025
We investigate the boundary trace operators that naturally correspond to H ( curl , Ω ) , namely the tangential and twisted tangential trace, where Ω ⊆ 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 ( curl , Ω ) 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.