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

页码：1097 / 1120

页数：24

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