# Gradient Young measures, varifolds, and a generalized Willmore functional

created by masnou on 20 Dec 2011
modified on 29 Oct 2012

[BibTeX]

Accepted Paper

Inserted: 20 dec 2011
Last Updated: 29 oct 2012

We consider the generalized Willmore functional 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 $L^1$, being $\Omega$ an open and bounded Lipschitz domain of $R^n$