Compensated Compactness for Differential Forms in Carnot Groups and Applications

Annalisa Baldi (1) , Bruno Franchi (1) , Nicoletta Tchou (2) , Maria Carla Tesi (1)

1 Dipartimento di Matematica [Bologna]
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we prove a compensated compactness theorem for differential forms of the intrinsic complex of a Carnot group. The proof relies on a $L^s$--Hodge decomposition for these forms. Because of the lack of homogeneity of the intrinsic exterior differential, Hodge decomposition is proved using the parametrix of a suitable 0-order Laplacian on forms.

Mots clés: Compensated compactness; Carnot groups; differential forms; currents; pseudodifferential operators on homogeneous groups

Domaines: Analyse fonctionnelle [math.FA]

Annalisa Baldi, Bruno Franchi, Nicoletta Tchou, Maria Carla Tesi. Compensated Compactness for Differential Forms in Carnot Groups and Applications. Advances in Mathematics, 2010, 223 (5), pp.1555-1607. ⟨hal-00298362⟩