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
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.
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页码:855 / 863
页数:9
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