(Non)uniqueness of minimizers in the least gradient problem

被引：11

作者：

Gorny, Wojciech ^{[1
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Warsaw, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 468卷 / 02期

关键词：

Least gradient problem; Minimal surfaces; Convex but non-strictly convex domains;

D O I：

10.1016/j.jmaa.2018.08.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Minimizers in the least gradient problem with discontinuous boundary data need not be unique. However, all of them have a similar structure of level sets. Here, we give a full characterization of the set of minimizers in terms of any one of them and discuss stability properties of an approximate problem. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：913 / 938

页数：26

共 50 条

[11] Non-Uniqueness of Minimizers for Strictly Polyconvex Functionals
Emanuele Nunzio Spadaro
[J]. Archive for Rational Mechanics and Analysis, 2009, 193 : 659 - 678
[12] LEAST GRADIENT PROBLEM ON ANNULI
Dweik, Samer
Gorny, Wojciech
[J]. ANALYSIS & PDE, 2022, 15 (03): : 699 - 725
[13] Least gradient problem with respect to a non-strictly convex norm
Gorily, Wojciech
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 200
[14] Local minimizers for a free gradient discontinuity problem in image segmentation
Carriero, M
Leaci, A
Tomarelli, F
[J]. VARIATIONAL METHODS FOR DISCONTINUOUS STRUCTURES, 2002, 51 : 67 - 80
[15] Uniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient
Zagatti, Sandro
[J]. JOURNAL OF CONVEX ANALYSIS, 2007, 14 (04) : 705 - 727
[16] Description of the Minimizers of Least Squares Regularized with l0-norm. Uniqueness of the Global Minimizer
Nikolova, Mila
[J]. SIAM JOURNAL ON IMAGING SCIENCES, 2013, 6 (02): : 904 - 937
[17] THE CONSTRAINED LEAST GRADIENT PROBLEM IN RN
STERNBERG, P
WILLIAMS, G
ZIEMER, WP
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 339 (01) : 403 - 432
[18] UNIQUENESS AND STABILITY FOR THE SOLUTION OF A NONLINEAR LEAST SQUARES PROBLEM
Huang, Meng
Xu, Zhiqiang
[J]. MATHEMATICS OF COMPUTATION, 2024, 93 (347) : 1247 - 1264
[19] Uniqueness and non-uniqueness in the non-axisymmetric direction problem
Kaiser, R.
[J]. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2012, 65 (03): : 347 - 360
[20] On the Uniqueness of Energy Minimizers in Finite Elasticity
Jeyabal Sivaloganathan
Scott J. Spector
[J]. Journal of Elasticity, 2018, 133 : 73 - 103

← 1 2 3 4 5 →