(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

[1] Existence and uniqueness of minimizers of general least gradient problems
Jerrard, Robert L.
Moradifam, Amir
Nachman, Adrian I.
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2018, 734 : 71 - 97
[2] Uniqueness of minimizers of weighted least gradient problems arising in hybrid inverse problems
Moradifam, Amir
Nachman, Adrian
Tamasan, Alexandru
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (01)
[3] Uniqueness of minimizers of weighted least gradient problems arising in hybrid inverse problems
Amir Moradifam
Adrian Nachman
Alexandru Tamasan
[J]. Calculus of Variations and Partial Differential Equations, 2018, 57
[4] Continuity of minimizers to weighted least gradient problems
Zuniga, Andres
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 178 : 86 - 109
[5] Existence and structure of minimizers of least gradient problems
Moradifam, Amir
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2018, 67 (03) : 1025 - 1037
[6] UNIQUENESS AND RADIAL SYMMETRY OF MINIMIZERS FOR A NONLOCAL VARIATIONAL PROBLEM
Lopes, Orlando
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2019, 18 (05) : 2265 - 2282
[7] UNIQUENESS AND SIGN PROPERTIES OF MINIMIZERS IN A QUASILINEAR INDEFINITE PROBLEM
Kaufmann, Uriel
Quoirin, Humberto Ramos
Umezu, Kenichiro
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2021, 20 (06) : 2313 - 2322
[8] Non-Uniqueness of Minimizers for Strictly Polyconvex Functionals
Spadaro, Emanuele Nunzio
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 193 (03) : 659 - 678
[9] EXISTENCE, UNIQUENESS, AND REGULARITY FOR FUNCTIONS OF LEAST GRADIENT
STERNBERG, P
WILLIAMS, G
ZIEMER, WP
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1992, 430 : 35 - 60
[10] LOCAL UNIQUENESS OF PROBLEM OF LEAST AREA
TOMI, F
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1973, 52 (04) : 312 - 318

← 1 2 3 4 5 →