arXiv Open Access 2021

A Compactness Result for the div-curl System with Inhomogeneous Mixed Boundary Conditions for Bounded Lipschitz Domains and Some Applications

Dirk Pauly Nathanael Skrepek

Lihat Sumber

Abstrak

For a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any $L^2$-bounded sequence of vector fields with $L^2$-bounded rotations and $L^2$-bounded divergences as well as $L^2$-bounded tangential traces on one part of the boundary and $L^2$-bounded normal traces on the other part of the boundary, contains a strongly $L^2$-convergent subsequence. This generalises recent results for homogeneous mixed boundary conditions by the first author and collaborators. As applications we present a related Friedrichs/Poincare 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.

Topik & Kata Kunci

math.AP math.FA

Penulis (2)

Dirk Pauly

Nathanael Skrepek

Format Sitasi

APA MLA BibTeX

Pauly, D., Skrepek, N. (2021). A Compactness Result for the div-curl System with Inhomogeneous Mixed Boundary Conditions for Bounded Lipschitz Domains and Some Applications. https://arxiv.org/abs/2103.06087

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓