Two isoperimetric inequalities for the Sobolev constant

被引：4

作者：

Carroll, Tom ^{[1
]}

Ratzkin, Jesse ^{[2
]}

机构：

[1] Natl Univ Ireland Univ Coll Cork, Dept Math, Cork, Ireland

[2] Univ Cape Town, Dept Math & Appl Math, ZA-7701 Rondebosch, South Africa

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2012年 / 63卷 / 05期

关键词：

Sobolev constant; Dirichlet eigenvalue; torsional rigidity; Schwarz Lemma; PAYNE-RAYNER TYPE; 1ST EIGENFUNCTION; MEMBRANE; VERSIONS; BOUNDS;

D O I：

10.1007/s00033-012-0198-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalizes an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.

引用

页码：855 / 863

页数：9

共 50 条

[21] On the best constant of Hardy-Sobolev inequalities
Adimurthi
Filippas, Stathis
Tertikas, Achilles
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (08) : 2826 - 2833
[22] Isoperimetric and Sobolev inequalities for Carnot-Caratheodory spaces and the existence of minimal surfaces
Garofalo, N
Nhieu, DM
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1996, 49 (10) : 1081 - 1144
[23] The effect of curvature on the best constant in the Hardy–Sobolev inequalities
N. Ghoussoub
F. Robert
[J]. Geometric & Functional Analysis GAFA, 2006, 16 : 1201 - 1245
[24] Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey
Xavier Cabré
[J]. Chinese Annals of Mathematics, Series B, 2017, 38 : 201 - 214
[25] Isoperimetric, Sobolev, and Eigenvalue Inequalities via the Alexandroff-Bakelman-Pucci Method: A Survey
Cabre, Xavier
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2017, 38 (01) : 201 - 214
[26] Isoperimetric, Sobolev, and Eigenvalue Inequalities via the Alexandroff-Bakelman-Pucci Method: A Survey
Xavier CABR
[J]. Chinese Annals of Mathematics,Series B, 2017, (01) : 201 - 214
[27] The weighted isoperimetric-type and Sobolev-type inequalities for hypersurfaces in Carnot groups
He, Guoqing
Zhao, Peibiao
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 135 : 35 - 56
[28] The sharp Sobolev and isoperimetric inequalities split twice (vol 211, pg 417, 2007)
Xiao, Jie
[J]. ADVANCES IN MATHEMATICS, 2015, 268 : 906 - 914
[29] ISOPERIMETRIC PROBLEMS AND SOBOLEV SPACES
AUBIN, T
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1975, 280 (05): : 279 - 281
[30] Best constant in Sobolev trace inequalities on the half-space
Nazaret, Bruno
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 65 (10) : 1977 - 1985

← 1 2 3 4 5 →