Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
type: Item
instance of: scholarly article
title: Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
zbMATH Open document ID: 0578.46028
DOI: 10.1016/0022-1236(85)90079-5
published in: Journal of Functional Analysis
publication date: 1985-01-01T00:00:00Z
review text: The well known equivalence of the Sobolev inequality and the isoperimetric inequality can be substantially generalized to set up an equivalence of certain other analytic inequalities with geometric inequalities involving Riemannian volume and surface measure. We exploit a special case of these equivalences to give log-Sobolev inequalities for Riemannian manifolds. Some applications to Schrödinger equations are also given.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 3925566
zbMATH Keywords: equivalence of the Sobolev inequality and the isoperimetric
zbMATH Keywords: inequality
zbMATH Keywords: Riemannian volume
zbMATH Keywords: surface measure
zbMATH Keywords: log-Sobolev inequalities for Riemannian manifolds
zbMATH Keywords: Schrödinger equations
zbMATH Keywords: equivalence of the Sobolev inequality and the isoperimetric inequality
Wikidata QID: Q105583514
author: Oscar S. Rothaus
MaRDI profile type: Publication
full work available at URL: 0022-1236(85)90079-5
OpenAlex ID: W2038486299
cites work: Problèmes isoperimetriques et espaces de Sobolev
cites work: The spaces \(L^ p\), with mixed norm
cites work: Q5565773
cites work: Logarithmic Sobolev Inequalities
cites work: Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere
cites work: The isoperimetric inequality
cites work: Lower bounds for eigenvalues of regular Sturm-Liouville operators and the logarithmic Sobolev inequality
cites work: Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities
cites work: Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
description: scientific article; zbMATH DE number 3925566