Sharp Stability of Some Spectral Inequalities

被引：31

作者：

Brasco, Lorenzo ^{[1
]}

Pratelli, Aldo ^{[2
]}

机构：

[1] Univ Aix Marseille 1, Lab Anal, Probabilites UMR6632, CMI 39, F-13453 Marseille 13, France

[2] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2012年 / 22卷 / 01期

基金：

欧洲研究理事会;

关键词：

Stability for eigenvalues; Krahn-Szego inequality; Szego-Weinberger inequality; isoperimetric inequalities;

D O I：

10.1007/s00039-012-0148-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work we review two classical isoperimetric inequalities involving eigenvalues of the Laplacian, both with Dirichlet and Neumann boundary conditions. The first one is classically attributed to Krahn and P. Szego and asserts that among sets of given measure, the disjoint union of two balls with the same radius minimizes the second eigenvalue of the Dirichlet-Laplacian, while the second one is due to G. SzegA and Weinberger and deals with the maximization of the first non-trivial eigenvalue of the Neumann-Laplacian. New stability estimates are provided for both of them.

引用

页码：107 / 135

页数：29

共 18 条

[1]

[Anonymous], 1962, METHODS MATH PHYS

[2]

ASHBAUGH M.S., 2007, P S PURE MATH AM MAT, V76, p[105, 1]

[3]

BHATTACHARYA T, 2001, ELECT J DIFFERENTIAL, V35

[4]

Bhattacharya T., 1999, Contemp. Math., V221, P31

[5]

Courant R., 1962, METHODS MATH PHYS, V2

[6] The sharp quantitative isoperimetric inequality [J].

Fusco, N. ;

Maggi, F. ;

Pratelli, A. .

ANNALS OF MATHEMATICS, 2008, 168 (03) :941-980

[7]

Fusco N, 2009, ANN SCUOLA NORM-SCI, V8, P51

[8]

GILBARG D., 2000, Elliptic Partial Differential Equations of Second Order, V2nd

[9]

Henrot A, 2005, MATH APPL-BERLIN, V48, P1

[10]

Henrot A, 2006, FRONT MATH, P1

← 1 2 →