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

Publication type:
Paper in peer-reviewed journals
Communications in Partial Differential Equations, vol. 39, pp. 1007-1031
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.
    author={Anne-Sophie Bonnet-BenDhia and Lucas Chesnel and Patrick 
           Ciarlet },
    title={T-coercivity for the Maxwell problem with sign-changing 
           coefficients },
    doi={10.1080/03605302.2014.892128 },
    journal={Communications in Partial Differential Equations },
    year={2014 },
    volume={39 },