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Journal Articles Communications in Partial Differential Equations Year : 2014

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

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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Dates and versions

hal-00762275 , version 1 (06-12-2012)

Identifiers

  • HAL Id : hal-00762275 , version 1

Cite

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet. T-coercivity for the Maxwell problem with sign-changing coefficients. Communications in Partial Differential Equations, 2014. ⟨hal-00762275⟩
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