Non-convex, non-local functionals converging to the total variation

被引：9
|
作者：
Brezis, Haim [1 ,2 ,3 ]
Hoai-Minh Nguyen [4 ]
机构：
[1] Hill Ctr, Dept Math, Busch Campus,110 Frelinghuysen Rd, Piscataway, NJ 08854 USA
[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
[3] Univ Paris 06, Lab Jacques Louis Lions, 4 Pl Jussieu, F-75252 Paris 05, France
[4] Ecole Polytech Fed Lausanne, SB MATHAA CAMA, Stn 8, CH-1015 Lausanne, Switzerland
来源：
COMPTES RENDUS MATHEMATIQUE | 2017年 / 355卷 / 01期
关键词：
SOBOLEV SPACES; GAMMA-CONVERGENCE; NORMS;
D O I：
10.1016/j.crma.2016.11.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present new results concerning the approximation of the total variation, integral(Omega)vertical bar del u vertical bar, of a function u by non-local, non-convex functionals of the form Lambda delta(u) = integral(Omega)integral(Omega)delta phi(vertical bar u(x) - u(y)vertical bar/delta)/vertical bar x-y vertical bar(d+1)dxdy, as delta -> 0, where Omega is a domain in R-d and phi : [0, +infinity) > [0, +infinity) is a non-decreasing function satisfying some appropriate conditions. The mode of convergence is extremely delicate, and numerous problems remain open. The original motivation of our work comes from Image Processing. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS.
引用
收藏
页码：24 / 27
页数：4
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