Isoperimetric Inequalities for Eigenvalues of Triangles

被引：12
|
作者：
Siudeja, Bartlomiej [1 ]
机构：
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2010年 / 59卷 / 03期
关键词：
eigenvalues; symmetrization; polarization; variational methods; polynomial inequalities; 1ST DIRICHLET EIGENVALUE; LOWER BOUNDS;
D O I：
10.1512/iumj.2010.59.3744
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Isoperimetric lower bounds for the first eigenvalue for the Dirichlet Laplacian on arbitrary triangles are proved using various symmetrization techniques. It is also shown that among triangles, the equilateral triangle maximizes the spectral gap and (under additional assumption) the ratio of the first two eigenvalues.
引用
收藏
页码：1097 / 1120
页数：24
相关论文
共 50 条
  • [1] Isoperimetric inequalities and eigenvalues
    Kahale, N
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 1997, 10 (01) : 30 - 40
  • [2] Isoperimetric Inequalities for Eigenvalues of the Laplacian
    Henrot, Antoine
    GEOMETRY OF PDES AND RELATED PROBLEMS, 2018, 2220 : 47 - 88
  • [3] Isoperimetric Inequalities for Eigenvalues of the Laplacian
    Benguria, Rafael D.
    ENTROPY AND THE QUANTUM II, 2011, 552 : 21 - 60
  • [4] Isoperimetric Inequalities for Eigenvalues of the Laplace Operator
    Benguria, Rafael D.
    Linde, Helmut
    FOURTH SUMMER SCHOOL IN ANALYSIS AND MATHEMATICAL PHYSICS: TOPIC IN SPECTRAL THEORY AND QUANTUM MECHANICS, 2008, 476 : 1 - 40
  • [5] Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrodinger operator
    Benguria, Rafael D.
    Linde, Helmut
    Loewe, Benjamin
    BULLETIN OF MATHEMATICAL SCIENCES, 2012, 2 (01) : 1 - 56
  • [6] SOME ISOPERIMETRIC INEQUALITIES FOR EIGENVALUES OF VIBRATING STRINGS
    BARNES, DC
    PACIFIC JOURNAL OF MATHEMATICS, 1969, 29 (01) : 43 - &
  • [7] ISOPERIMETRIC INEQUALITIES FOR ELASTICALLY BOUND MEMBRANES ON TRIANGLES AND QUADRALATERALS
    HERSCH, J
    SIGRIST, K
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1970, 21 (05): : 836 - &
  • [8] Rearrangement inequalities and applications to isoperimetric problems for eigenvalues
    Hamel, Francois
    Nadirashvili, Nikolai
    Russ, Emmanuel
    ANNALS OF MATHEMATICS, 2011, 174 (02) : 647 - 755
  • [9] Isoperimetric inequalities of the fourth order Neumann eigenvalues
    Yanlin Deng
    Feng Du
    Journal of Inequalities and Applications, 2020
  • [10] STABILITY OF ISOPERIMETRIC INEQUALITIES FOR LAPLACE EIGENVALUES ON SURFACES
    Karpukhin, Mikhail
    Nahon, Mickael
    Polterovich, Iosif
    Stern, Daniel
    JOURNAL OF DIFFERENTIAL GEOMETRY, 2025, 129 (02) : 415 - 490
12345