Time-harmonic Maxwell equations in the exterior of perfectly conducting, irregular obstacles (Q2757212)

The boundary value problem of total reflection of time-harmonic electromagnetic waves is considered in the exterior of perfectly conducting, irregular obstacles. More precisely, the boundary value problem for Maxwell's equations in exterior of some domain with a variant of the Silver-Müller radiation condition is studied. A Fredholm type alternative is shown to be valid by rather general assumptions on boundary regularity and regularity of the coefficients. The solvability theory is developed in suitably weighted spaces. A local compact embedding property is proved which in its turn is based on the global Maxwell compactness property (MCP). The appendix illustrates the theory by some examples.