Gradient Young measures, varifolds, and a generalized Willmore functional

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

2011-12-09

arxiv.org/abs/1112.2091v1

Mathematics

Optimization and Control

39 pages

Scientific paper

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.

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