WIAS Preprint No. 488, (1999)

Regularity of solutions of Maxwell's equations with mixed boundary conditions

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Authors

• Jochmann, Frank

2010 Mathematics Subject Classification

• 35Q60 35D10 35F15

Keywords

• Maxwell's equations, Regulariy of weak solutions, Mixed boundary-conditions

DOI

10.20347/WIAS.PREPRINT.488

Abstract

The subject of this paper are H^s and L^p-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 H^s(Ω) for sufficiently small s > 0. It follows from this regularity result that H^s(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 L^p -regularity-theorem for the transient equations is proved.

Appeared in

• Math. Methods Appl. Sci, 22 (1999), pp. 1255-1274

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