Some remarks on vector potentials for Maxwell's equations in space-time Carnot groups

In this paper we prove a $Gamma$-convergence result for time-depending variational functionals in a space-time Carnot group $RtimesG$ arising in the study of Maxwell's equations in the group. Indeed, a Carnot groups $G$ (a connected simply connected nilpotent stratified Lie group) can be endowed with a complex of ``intrinsic'' differential forms that provide the natural setting for a class of ``intrinsic'' Maxwell's equations. Our main results states precisely that a the vector potentials of a solution of Maxwell's equation in $RtimesG$ is a critical point of a suitable functional that is in turn a $Gamma$-limit of a sequence of analogous Riemannian functionals.