The regularity of the four time-harmonic vector fields composing any strong solution of the system obtained from Maxwell's curl equations and the constitutive relations in the interior of an inhomogeneous bianisotropic material are investigated. The results are given as interior Sobolev or Holder regularity. Possible local C-infinity regularity or local analyticity of the four vector fields are discussed, too. Each of these regularity results is obtained under specific conditions on the impressed current densities and on the constitutive parameters of the bianisotropic material considered, but it is shown that such conditions do not significantly limit the coverage of our analysis in terms of applications.
Regularity of time-harmonic electromagnetic fields in the interior of bianisotropic materials and metamaterials
RAFFETTO, MIRCO
2014-01-01
Abstract
The regularity of the four time-harmonic vector fields composing any strong solution of the system obtained from Maxwell's curl equations and the constitutive relations in the interior of an inhomogeneous bianisotropic material are investigated. The results are given as interior Sobolev or Holder regularity. Possible local C-infinity regularity or local analyticity of the four vector fields are discussed, too. Each of these regularity results is obtained under specific conditions on the impressed current densities and on the constitutive parameters of the bianisotropic material considered, but it is shown that such conditions do not significantly limit the coverage of our analysis in terms of applications.
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