Solenoidal and irrotational vector fields in $H^{-1}$ and related topics

Prof. Dirk Pauly

March 3, 2016, 1:45 p.m. S2 416-2

We present well known results for Maxwell’s equations on the $L^2$-level, such as vector potentials, Helmholtz decompositions, static solution theories, Maxwell estimates, and regular decompositions, on the not so popular $H^{-1}$-level.

Moreover, we compute the dual spaces of $R^{\circ}$ and $D^{\circ}$ and discuss regularity results, such as Necas' lemma.

At the end we might discuss some applications.

Abstract