A coarea-type formula for the relaxation of a generalized elastica functional

Simon Masnou (1) , Giacomo Nardi (2)

1 MMCS - Modélisation mathématique, calcul scientifique
2 LJLL - Laboratoire Jacques-Louis Lions

We consider in R^2 the generalized elastica functional defined, for smooth functions, as the p-elastica energies of the level lines integrated over all levels. Extending the functional to L1, we study its L1-lower semicontinuous envelope and we prove that, for any u in BV, the envelope at u can be represented by a coarea-type formula involving suitable collections of W2,p curves that cover the essential boundaries of the level sets of u.

Mots clés: elastica; curvature; relaxation; BV

Domaines: Optimisation et contrôle [math.OC]

Simon Masnou, Giacomo Nardi. A coarea-type formula for the relaxation of a generalized elastica functional. Journal of Convex Analysis, 2013, 20 (3), pp.617-653. ⟨hal-00649363⟩