Integral equations with modified fundamental solutions for exterior boundary value problems from electromagnetic wave theory

The application of the method of the modified fundamental solution of integral equations to exterior boundary value problems from the theory of electromagnetic waves was investigated. The modification of the fundamental solution for the scalar Helmholtz equation is presented. It is shown that this solution can be considered as a dyadic. The existence proofs for three electromagnetic boundary value problems are given. It is demonstrated that the addition of a suitable finite series for the fundamental solution is sufficient to obtain uniqueness.