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

10 Mar 2021  ·  Dirk Pauly, Nathanael Skrepek ·

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. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Analysis of PDEs Functional Analysis