Clifford algebras and Maxwell's equations in Lipschitz domains

An analogue of the Sommerfeld radiation condition for the Dirac operator

“…Nevertheless, as was shown in [7] this condition can be represented in a more elegant form. We note that the expression which appears in (14) can be rewritten as follows…”

“…Thus, in order to be able to apply (16) instead of (14), we should prove that if f belongs to ker D ν (R 3 \ Ω) and satisfies (16) then it decreases at infinity. Following arguments from [7] we prove this.…”

“…The introduction of the radiation condition in the form (14) allowed us to obtain a very simple proof of the Cauchy integral formula for the exterior domain. Nevertheless, as was shown in [7] this condition can be represented in a more elegant form. We note that the expression which appears in (14) can be rewritten as follows…”

A spin integral equation for electromagnetic and acoustic scattering

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Transmission boundary problems for Dirac operators on Lipschitz domains and applications to Maxwell’s and Helmholtz’s equations

“…Given a bounded Lipschitz domain Ω ⊆ R 3 , k ∈ C, and p ∈ (1, ∞), the following equivalence holds (cf. [Mi94] for results of this type): The following result, which is the counterpart of (4.40) for the unbounded domain Ω − , has been proved in [McM99].…”