A semi derivation lemma on BV functions

Filippo Santambrogio (1) , François-Xavier Vialard (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CMLA - Centre de Mathématiques et de Leurs Applications

This paper presents a proof of a derivation lemma on the space of BV functions. The origin of this question can be found in the context of the image matching in the framework of large deformation diffeomorphisms. To compute the geodesic equations on the space of diffeomorphisms, one needs this derivation lemma. It gives also the structure of the initial momentum, which is the central tool in the Hamiltonian formulation of geodesic equations.

Mots clés: SBV; Lipschitz domains; strong approximation in BV

Domaines: Analyse fonctionnelle [math.FA]

Filippo Santambrogio, François-Xavier Vialard. A semi derivation lemma on BV functions. 2008. ⟨hal-00317751⟩