This is an interesting paper examining the transmission of DC current as ω→0 in the telegrapher's equation using the Heaviside step function.
Abstract—We explore the question of how direct current (DC) power is transmitted by electromagnetic fields in TEM/Quasi-TEM structures despite the static curl laws ∇ × E = 0 and ∇ × H = J. In this work we treat DC as the long-time limit of a causal step excitation.