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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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Published in: | Communications in partial differential equations 2014-06, Vol.39 (6), p.1007-1031 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0360-5302 1532-4133 |
DOI: | 10.1080/03605302.2014.892128 |