A RELATIVE ISOPERIMETRIC INEQUALITY-Reference-Cited by-同舟云学术

A RELATIVE ISOPERIMETRIC INEQUALITY

Published:2012-06 Issue:03 Volume:14 Page:1250023
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

BROCK FRIEDEMANN¹,WILLEM MICHEL²

Affiliation:

1. Department of Mathematics, American University of Beirut, Bliss Street, P. O. Box: 11-0236, Beirut, Lebanon

2. Département Mathématique, Université Catholique de Louvain, Chemin du Cyclotron, 2, 1348 Louvain-la-Neuve, Belgium

Abstract

We prove that, if Ω is an open subset of ℝN with finite measure, there exists a hyperplane H through 0 such that the measure of Ω ∩ H is less than the measure of B ∩ H, where B is the open ball with center 0 having the same measure as Ω. An application is given to the optimal Poincaré inequality on BV(Ω).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021919971250023X

Reference11 articles.

1. Some critical minimization problems for functions of bounded variations

2. Extremal functions in Poincaré-Sobolev inequalities for functions of bounded variation

3. On the Busemann-Petty problem for perturbations of the ball

4. Circulation integrals and critical Sobolev spaces: problems of optimal constants

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Variable exponents and grand Lebesgue spaces: Some optimal results;Communications in Contemporary Mathematics;2015-10-29

2. Analytical inequalities and isoperimetric constants;Portugaliae Mathematica;2014

3. The Longest Shortest Fence and Sharp Poincaré–Sobolev Inequalities;Archive for Rational Mechanics and Analysis;2012-07-31