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Potenze frazionarie e teoria della interpolazione per operatori lineari multivoci ed applicazioni Differential forms in Carnot groups: a variational approach

Author(s): Annalisa Baldi

Journal: Bruno Pini Mathematical Analysis Seminar
ISSN 2240-2829

Volume: 2;
Issue: 1;
Date: 2011;
Original page

Keywords: Carnot groups | differential forms | gamma-convergence

Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex of ``intrinsic'' differential forms. In this paper we want to provide an evidence of the intrinsic character of Rumin's complex, in the spirit of the Riemannian approximation, like in e.g., the notes of Gromov (Textes Mathématiques 1981) and in Rumin (Geom. Funct. Anal.,2000) . More precisely, we want to show that the intrinsic differential is a limit of suitably weighted usual first order de Rham differentials. As an application, we prove that the L^2-energies associated to classical Maxwell's equations in R^n Gamma-converges to the L^2-energies associated to an ''intrinsic'' Maxwell's equation in a free Carnot group.
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