A compactness result for the div-curl system with inhomogeneous mixed boundary conditions for bounded Lipschitz domains and some applications

Research output: Contribution to journalResearch articleContributedpeer-review


  • Dirk Pauly - , Institute of Analysis, TUD Dresden University of Technology (Author)
  • Nathanael Skrepek - , Freiberg University of Mining and Technology (Author)


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.


Original languageEnglish
Pages (from-to)505-519
Number of pages15
JournalAnnali dell'Universita di Ferrara
Issue number2
Publication statusPublished - Nov 2023

External IDs

ORCID /0000-0003-4155-7297/work/145224255


ASJC Scopus subject areas


  • Compact embeddings, Div-curl system, Inhomogeneous boundary conditions, Mixed boundary conditions