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

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Contributors

Abstract

We investigate the boundary trace operators that naturally correspond to H(curl,Ω), namely the tangential and twisted tangential trace, where Ω⊆R3. 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 L2 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.

Details

Original languageEnglish
Article number129548
JournalJournal of mathematical analysis and applications
Volume550
Issue number1
Publication statusPublished - 1 Oct 2025
Peer-reviewedYes

External IDs

ORCID /0000-0003-4155-7297/work/186184522

Keywords

ASJC Scopus subject areas

Keywords

  • Boundary traces, Density, Lipschitz boundary, Lipschitz domains, Maxwell's equations, Tangential traces