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Some Remarks on Vector Potentials for Maxwell's Equations in Space-Time Carnot Groups

Annalisa BaldiBruno Franchi — 2012

Bollettino dell'Unione Matematica Italiana

In this paper we prove a Γ -convergence result for time-depending variational functionals in a space-time Carnot group × 𝔾 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...

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