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arXiv:1707.00019 [math.AP]AbstractReferencesReviewsResources

A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains and a Corresponding Generalized $\mathrm{A}_{0}^{*}$-$\mathrm{A}_{1}$-Lemma in Hilbert Spaces

Dirk Pauly

Published 2017-06-30Version 1

We prove global and local versions of the so called div-curl-lemma, also known as compensated compactness, for mixed boundary conditions as well as bounded weak Lipschitz domains in 3D and weak Lipschitz interfaces. We will generalize our results using an abstract Hilbert space setting, which shows corresponding results to hold in arbitrary dimensions as well as for various differential operators. The crucial tools are Hilbert complexes and related compact embeddings.

Comments: key words: div-curl-lemma, compensated compactness, mixed boundary conditions, weak Lipschitz domains, Maxwell's equations
Categories: math.AP, math-ph, math.FA, math.MP
Subjects: 35B27, 35Q61, 47B07, 46B50
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