Lipschitz spaces and Poincaré inequalities
type: Item
instance of: scholarly article
title: Lipschitz spaces and Poincaré inequalities
zbMATH Open document ID: 0859.58009
author: Thierry Coulhon
published in: Journal of Functional Analysis
publication date: 1997-04-07T00:00:00Z
review text: The author shows that in the setting of infinite graphs and non-compact Riemannian manifolds, the suitable families of Poincaré inequalities yield global embeddings of Sobolev spaces into Lipschitz spaces, as well as Trudinger type inequalities. This applies for example to cocompact coverings and to manifolds that are roughly isometric to a manifold with nonnegative Ricci curvature. In this process, the author gives several reformulations of the Sobolev inequalities, and in particular shows their equivalence with some \(L^p\) Faber-Krahn inequalities. An interpretation of some of the obtained results is also given in terms of distances on graphs associated with the \(L^p\) norm of the gradient.
Mathematics Subject Classification ID: 58E35
zbMATH DE Number: 871738
zbMATH Keywords: Poincaré inequalities
zbMATH Keywords: Lipschitz spaces
zbMATH Keywords: Trudinger type inequalities
zbMATH Keywords: Sobolev inequalities
zbMATH Keywords: Faber-Krahn inequalities
zbMATH Keywords: \(L^ p\) norm
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
full work available at URL: jfan.1996.0022
OpenAlex ID: W1974167482
DOI: 10.1006/JFAN.1996.0022
description: scientific article; zbMATH DE number 871738