Elliptic and Parabolic Equations - Abstract

Schmidt, Gunther

Existence and uniqueness of solution for a system of Helmholtz equations

The talk is devoted to the scattering of a plane wave obliquely illuminating a periodic structure. Maxwell's equations can be transformed to a transmission problem for a system of Helmholtz equations with piecewise continuous complex-valued coefficients. Using integral equation techniques we study the existence and uniqueness of solutions under general assumptions on material parameters. In particular, new results for materials with negative permittivity or permeability are established.