Complementary formulations in steady-state eddy-current theory

The symmetry and the duality inherent in the Maxwell equations result in the existence of complementary formulations. This can be used to derive bilateral estimates for quantities like the resistance or the reluctance, in static situations. Whether similar bounds can be obtained for both the real and imaginary parts of the impedance in steady-state eddy-current problems is a controversial and still open question. The author reviews the basics of approximation theory, as applied to eddy-current equations and looks for proof methods that could be used to assert the existence of bilateral bounds, but finds them unable to do this.