The perimeter inequality under Steiner symmetrization:: Cases of equality

被引:57
作者
Chlebík, M
Cianchi, A
Fusco, N
机构
[1] Max Planck Inst Math Nat Wissensch, Leipzig, Germany
[2] Univ Florence, I-50121 Florence, Italy
[3] Univ Naples Federico II, I-80138 Naples, Italy
关键词
D O I
10.4007/annals.2005.162.525
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Steiner symmetrization is known not to increase perimeter of sets in R-n. The sets whose perimeter is preserved under this symmetrization are characterized in the present paper.
引用
收藏
页码:525 / 555
页数:31
相关论文
共 21 条
[11]   Functions of bounded variation and rearrangements [J].
Cianchi, A ;
Fusco, N .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 165 (01) :1-40
[12]  
De Giorgi E., 1954, ANN MAT PUR APPL, V4, P191
[13]  
Evans L. C., 2018, Measure Theory and Fine Properties of Functions
[14]  
Federer H., 2014, GEOMETRIC MEASURE TH
[15]  
Giaquinta M., 1998, Cartesian Currents in the Calculus of Variations, Part I: Cartesian Currents, Part II: Variational Integrals
[17]   SHARP CONSTANTS IN THE HARDY-LITTLEWOOD-SOBOLEV AND RELATED INEQUALITIES [J].
LIEB, EH .
ANNALS OF MATHEMATICS, 1983, 118 (02) :349-374
[18]  
Steiner J., 1838, J REINE ANGEW MATH, V18, P281
[19]  
Talenti G., 1993, STANDARD ISOPERIMETR, P73, DOI DOI 10.1016/B978-0-444-89596-7.50008-0
[20]  
Volpert A. I., 1967, Maths. USSR Sb., V2, P225, DOI [DOI 10.1070/SM1967V002N02ABEH002340, 10.1070/SM1967v002n02ABEH002340]