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

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