The time dependent Maxwell system with measurable coefficients in Lipschitz domains

Semigroup theory is employed to study inhomogeneous boundary conditions for the time-dependent Maxwell equations with anisotropic material parameters in a non-smooth domain. Only boundedness and measurability of the coefficients are assumed, and the boundary data is assumed to be time independent. W...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 452; no. 2; pp. 941 - 956
Main Author Stachura, Eric
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.08.2017
Subjects
Anisotropy
Lipschitz domains
Maxwell system
Sobolev spaces
Sobolev spaces
Anisotropy
Maxwell system
Lipschitz domains
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Summary:Semigroup theory is employed to study inhomogeneous boundary conditions for the time-dependent Maxwell equations with anisotropic material parameters in a non-smooth domain. Only boundedness and measurability of the coefficients are assumed, and the boundary data is assumed to be time independent. When the material parameters are positive definite, a higher order Sobolev theory is developed for the time-dependent Maxwell system.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.03.052