*Submitted Paper*

**Inserted:** 21 jul 2008

**Year:** 2008

**Abstract:**

This paper presents a proof of a derivation lemma on the space of BV functions, mainly of the function $t\mapsto \int f\circ \phi_t g$, where $\phi_t$ is the flow of a vector field. 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 result, which also gives the structure of the initial momentum, i.e. the central tool in the Hamiltonian formulation of geodesic equations.

**Keywords:**
SBV, Lipschitz domains, strong approximation in BV

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