Regularity of solutions of Maxwell's equations with mixed boundary conditions
- Jochmann, Frank
2010 Mathematics Subject Classification
- 35Q60 35D10 35F15
- Maxwell's equations, Regulariy of weak solutions, Mixed boundary-conditions
The subject of this paper are 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 nonlinear conductivity is present a Lp -regularity-theorem for the transient equations is proved.
- Math. Methods Appl. Sci, 22 (1999), pp. 1255-1274