Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains
Year: 2025
Type: article
Abstract: 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.
Authors: Nathanael Skrepek, Dirk Pauly
Institutions: University of Twente, Technische Universität Dresden
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4409136506