A general compactness theorem in G(S)BD

Antonin Chambolle (1, 2) , Vito Crismale (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
3 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

We give a new, simpler proof of a compactness result in GSBDp , p > 1, by the same authors, which is also valid in GBD (the case p = 1), and shows that bounded sequences converge a.e., after removal of a suitable sequence of piecewise innitesimal rigid motions, subject to a fixed partition.

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Science des matériaux [cond-mat.mtrl-sci]

Antonin Chambolle, Vito Crismale. A general compactness theorem in G(S)BD. Indiana University Mathematics Journal, inPress. ⟨hal-03807668⟩