A Compactness Result for the div-curl System with Inhomogeneous Mixed Boundary Conditions for Bounded Lipschitz Domains and Some Applications · arXivDesk
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
Nearby in the stack
-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 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.