Sebastian Bauer, Dirk Pauly, Michael Schomburg
Published 2018-09-04Version 1
It is proved that the space of differential q-forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable q-forms. Mixed boundary conditions on weak Lipschitz domains are considered. Furthermore, canonical applications such as Maxwell estimates, Helmholtz decompositions and a static solution theory are proved.
Comments: key words: Maxwell compactness property, weak Lipschitz domain, Maxwell estimate, Helmholtz decomposition, electro-magneto statics, mixed boundary conditions, vector potentials
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
A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains
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