Gradient Young measures, varifolds, and a generalized Willmore functional

Simon Masnou (1) , Giacomo Nardi (2)

1 ICJ - Institut Camille Jordan
2 LJLL - Laboratoire Jacques-Louis Lions

Being Omega an open and bounded Lipschitz domain of R^n, we consider the generalized Willmore functional on Omega defined, for smooth functions, as the p-Willmore energy of each isolevel set integrated over all levels. We propose a new framework, that combines varifolds and Young measures, to study the relaxation of this functional in BV(Omega) with respect to the strong topology of L^1.

Mots clés: Willmore; mean curvature; relaxation; BV

Domaines: Optimisation et contrôle [math.OC]

Simon Masnou, Giacomo Nardi. Gradient Young measures, varifolds, and a generalized Willmore functional. Advances in Calculus of Variations, 2013, 6 (4), pp.433-482. ⟨hal-00649377v2⟩