A Bidimensional Electromagnetic Problem
Michel Crouzeix, Jean Descloux · SIAM Journal on Mathematical Analysis · 1990
Electric alternating currents running in a system of infinite cylindrical parallel conductors generate an electromagnetic field, which is defined by a potential $\varphi :\mathbb{R}^2 \to \mathbb{C}$. $\varphi $ is harmonic in the exterior domain and satisfies a Helmholtz equation in the cross sections of the conductors. The asymptotic properties of $\varphi $ as the frequency tends to infinity, in particular the boundary layers due to the skin effect, are studied.