Gradient Young measures, varifolds, and a generalized Willmore functional

被引:4
作者
Masnou, Simon [1 ]
Nardi, Giacomo [2 ]
机构
[1] Univ Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, F-69622 Villeurbanne, France
[2] Univ Paris 06, CNRS, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France
关键词
Willmore; mean curvature; relaxation; BV; varifolds; Young measures; 2ND FUNDAMENTAL FORM; SURFACES; REPRESENTATION; CALCULUS;
D O I
10.1515/acv-2011-0014
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Being Omega an open and bounded Lipschitz domain of R-n, we consider the generalized Willmore functional defined on L-1(Omega) as F(u) = integral(Omega)vertical bar del u vertical bar (alpha + beta vertical bar div del u/vertical bar del u vertical bar vertical bar(p)) dx if u is an element of C-2(Omega), and F(u) = +infinity else, where p > 1, alpha > 0, beta >= 0. We propose a new framework that combines varifolds and Young measures to study the relaxation of F in BV(Omega) with respect to the strong topology of L-1.
引用
收藏
页码:433 / 482
页数:50
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