Well-posedness of domain integral equations for a dielectric object in homogeneous background (Q1000845)

This paper deals with various properties of a dielectric object. There are analyzed the integro-differential equations for the contrast current density, for the electric field and for the generalized electric-flux density and it is established the existence of bounded inverses with respect to various function spaces. The authors show that these equations can be reduced to a Fredholm integral equation of the second kind with a unique solution. It is also argued that the problems are well-posed with respect to three different function spaces and that the conditions for the well-posedness of the equations are identical. The proofs strongly rely on the Riesz-Fredholm theory, combined with the Helmholtz decomposition and the Sobolev embedding theorem.