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

Gradient Young measures, varifolds, and a generalized Willmore functional