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T-coercivity for the Maxwell problem with sign-changing coefficients

Anne-Sophie Bonnet-Ben Dhia 1 Lucas Chesnel 1, 2 Patrick Ciarlet 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : 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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Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet. T-coercivity for the Maxwell problem with sign-changing coefficients. Communications in Partial Differential Equations, Taylor & Francis, 2014. ⟨hal-00762275⟩

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