Gradient Young measures, varifolds, and a generalized Willmore\n functional

2011/12/09 by Simon Masnou, Masnou, Simon, Giacomo Nardi +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1112.2091

openalex publication_date 2011/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Being Omega an open and bounded Lipschitz domain of Rⁿ, we consider the\ngeneralized Willmore functional on Omega defined, for smooth functions, as the\np-Willmore energy of each isolevel set integrated over all levels. We propose a\nnew framework, that combines varifolds and Young measures, to study the\nrelaxation of this functional in BV(Omega) with respect to the strong topology\nof L¹.\n

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• Mean curvature and sharp Willmore inequalities in metric spaces
• The L¹ gradient flow of a generalized scale invariant Willmore energy for radially non increasing functions

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