A Transmission Problem in the Scattering of Electromagnetic Waves by a Penetrable Object

Abstract

Layer-potential techniques are used to study a transmission problem arising in the scattering of electromagnetic waves by a penetrable object. The method proposed does not involve the use of the calculus of pseudodifferential operators and hence it can be applied in domains with very little regularity. The solutions are represented as a combination of a curl and a double curl of a single layer-potential operator. The work relies on the important harmonic-analysis tools developed in recent years to study boundary-value problems in domains with minimal regularity assumptions.