For a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any L2-bounded sequence of vector fields with L2-bounded rotations and L2-bounded divergences as well as L2-bounded tangential traces on one part of the boundary and L2-bounded normal traces on the other part of the boundary, contains a strongly L2-convergent subsequence. This generalises recent results for homogeneous mixed boundary conditions in Bauer et al. (SIAM J Math Anal 48(4):2912-2943, 2016) Bauer et al. (in: Maxwell’s Equations: Analysis and Numerics (Radon Series on Computational and Applied Mathematics 24), De Gruyter, pp. 77-104, 2019). As applications we present a related Friedrichs/Poincaré type estimate, a div-curl lemma, and show that the Maxwell operator with mixed tangential and impedance boundary conditions (Robin type boundary conditions) has compact resolvents.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:91612 |
| Date | 04 June 2024 |
| Creators | Pauly, Dirk, Skrepek, Nathanael |
| Publisher | Springer |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 1827-1510, 10.1007/s11565-022-00444-3, info:eu-repo/grantAgreement/Europäische Union/H2020 | MSCA-ITN-ETN/765579//Control of flexible structures and fluid-structure interactions/ConFlex |
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