  In this work, we are interested in the analysis of time-harmonic Maxwell's
equations in presence of a conical tip of a material with negative dielectric
constants. When these constants belong to some critical range, the
electromagnetic field exhibits strongly oscillating singularities at the tip
which have infinite energy. Consequently Maxwell's equations are not well-posed
in the classical $L^2$ framework. The goal of the present work is to provide an
appropriate functional setting for 3D Maxwell's equations when the dielectric
permittivity (but not the magnetic permeability) takes critical values.
Following what has been done for the 2D scalar case, the idea is to work in
weighted Sobolev spaces, adding to the space the so-called outgoing propagating
singularities. The analysis requires new results of scalar and vector potential
representations of singular fields. The outgoing behaviour is selected via the
limiting absorption principle.
