The results of this paper can be extended to more general Lipschitz domains by leveraging the established functional framework for Maxwell's equations on Lipschitz domains, as discussed in the context of the paper. The key steps involve generalizing the definitions of Sobolev spaces and boundary integral operators to accommodate non-polyhedral geometries. This includes ensuring that the tangential trace operators, trace spaces, and relevant surface differential operators are appropriately defined for these more complex domains.
Moreover, the coercivity and compactness results proven for the magnetic field integral equation (MFIE) on polyhedra can be adapted to Lipschitz domains by demonstrating that the necessary assumptions regarding the wave number and the geometry of the boundary still hold. The extension would also require a careful analysis of the singularities of the solutions in the context of the geometry of the Lipschitz domain, as these singularities can affect the convergence rates and stability of the numerical methods employed. By following the methodologies outlined in the paper and applying them to more general Lipschitz domains, one can establish a robust theoretical foundation for the application of boundary element methods (BEMs) in a wider range of practical scenarios.