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 language | English |
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| Article number | 129548 |
| Journal | Journal of mathematical analysis and applications |
| Volume | 550 |
| Issue number | 1 |
| Publication status | Published - 1 Oct 2025 |
| Peer-reviewed | Yes |
External IDs
| ORCID | /0000-0003-4155-7297/work/186184522 |
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Keywords
ASJC Scopus subject areas
Keywords
- Boundary traces, Density, Lipschitz boundary, Lipschitz domains, Maxwell's equations, Tangential traces