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.

A. Baldi, B. Franchi (2012). Some remarks on vector potentials for Maxwell's equations in space-time Carnot groups. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 5(9)(2), 337-355.

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

BALDI, ANNALISA;FRANCHI, BRUNO
2012

Abstract

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.
2012
A. Baldi, B. Franchi (2012). Some remarks on vector potentials for Maxwell's equations in space-time Carnot groups. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 5(9)(2), 337-355.
A. Baldi; B. Franchi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/117917
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