Regularity of weak solutions of Maxwell's equations with mixed boundary-conditions
Frank Jochmann · Mathematical Methods in the Applied Sciences · 1999
In this paper global Hs- and Lp-regularity results for the stationary and transient Maxwell equations with mixed boundary conditions in a bounded spatial domain are proved. First it is shown that certain elements belonging to the fractional-order domain of the Maxwell operator belong to Hs(Ω) for sufficiently small s > 0. It follows from this regularity result that Hs(Ω) is an invariant subspace of the unitary group corresponding to the homogeneous Maxwell equations with mixed boundary conditions. In the case that a possibly non-linear conductivity is present a Lp-regularity theorem for the transient equations is proved. Copyright © 1999 John Wiley & Sons, Ltd.