Abstract
AbstractFor a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any $$\mathsf {L}_{}^{2}$$
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-bounded sequence of vector fields with $$\mathsf {L}_{}^{2}$$
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-bounded rotations and $$\mathsf {L}_{}^{2}$$
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-bounded divergences as well as $$\mathsf {L}_{}^{2}$$
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-bounded tangential traces on one part of the boundary and $$\mathsf {L}_{}^{2}$$
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-bounded normal traces on the other part of the boundary, contains a strongly $$\mathsf {L}_{}^{2}$$
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-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.
Funder
Technische Universität Dresden
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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