The optimal problems for torsional rigidity

被引：0
作者：
Yang, Jin [1 ]
Wei, Zhenzhen [1 ]
机构：
[1] Hubei Minzu Univ, Dept Math, Enshi 445000, Hubei, Peoples R China
来源：
AIMS MATHEMATICS | 2021年 / 6卷 / 05期
基金：
中国国家自然科学基金;
关键词：
geominimal surface area; Petty bodies; torsional rigidity; torsional measure; mixed torsional rigidity; MINKOWSKI-FIREY THEORY; AFFINE; INEQUALITIES;
D O I：
10.3934/math.2021271
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the optimization problems associated with the nonhomogeneous and homogeneous Orlicz mixed torsional rigidities by investigating the properties of the corresponding mixed torsional rigidity. As the main results, the existence and the continuity of the solutions to these problems are proved.
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收藏
页码：4597 / 4613
页数：17
相关论文
共 47 条
[1]  
[Anonymous], 1937, Mat. Sb. (N. S.)
[2]  
[Anonymous], 1974, Geom. Dedicata
[3]  
Böröczky KJ, 2013, J DIFFER GEOM, V95, P215, DOI 10.4310/jdg/1376053446
[4]   The Lp-Busemann-Petty centroid inequality [J].
Campi, S ;
Gronchi, P .
ADVANCES IN MATHEMATICS, 2002, 167 (01) :128-141
[5]   On the reverse Orlicz Busemann-Petty centroid inequality [J].
Chen, Fangwei ;
Zhou, Jiazu ;
Yang, Congli .
ADVANCES IN APPLIED MATHEMATICS, 2011, 47 (04) :820-828
[6]   Brunn-Minkowski inequalities for variational functionals and related problems [J].
Colesanti, A .
ADVANCES IN MATHEMATICS, 2005, 194 (01) :105-140
[7]   The Minkowski Problem for Torsional Rigidity [J].
Colesanti, Andrea ;
Fimiani, Michele .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (03) :1013-1039
[8]  
Fenchel W., 1938, Dan. Vid. Selsk. Mat. Fys. Medd., V16, P1
[9]   General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem II [J].
Gardner, Richard J. ;
Hug, Daniel ;
Xing, Sudan ;
Ye, Deping .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (01)
[10]   General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem I [J].
Gardner, Richard J. ;
Hug, Daniel ;
Weil, Wolfgang ;
Xing, Sudan ;
Ye, Deping .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (01)
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