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T-Coercivity for the Maxwell Problem with Sign-Changing Coefficients

In this paper, we study the time-harmonic Maxwell problem with sign-changing permittivity and/or permeability, set in a domain of ℝ 3 . We prove, using the T -coercivity approach, that the well-posedness of the two canonically associated scalar problems, with Dirichlet and Neumann boundary condition...

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Bibliographic Details
Published in:Communications in partial differential equations 2014-06, Vol.39 (6), p.1007-1031
Main Authors: Dhia, Anne-Sophie Bonnet-Ben, Chesnel, Lucas, Ciarlet, Patrick
Format: Article
Language:English
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Summary:In this paper, we study the time-harmonic Maxwell problem with sign-changing permittivity and/or permeability, set in a domain of ℝ 3 . We prove, using the T -coercivity approach, that the well-posedness of the two canonically associated scalar problems, with Dirichlet and Neumann boundary conditions, implies the well-posedness of the Maxwell problem. This allows us to give simple and sharp criteria, obtained in the study of the scalar cases, to ensure that the Maxwell transmission problem between a classical dielectric material and a negative metamaterial is well-posed.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2014.892128