Balls have the worst best Sobolev inequalities. II: Variants and extensions
type: Item
instance of: scholarly article
title: Balls have the worst best Sobolev inequalities. II: Variants and extensions
zbMATH Open document ID: 1135.46016
author: Francesco Maggi
author: Cédric Villani
published in: Calculus of Variations and Partial Differential Equations
publication date: 2007-11-28T00:00:00Z
review text: This is the sequel to [J.~Geom. Anal. 15, No. 1, 83--121 (2005; Zbl 1086.46021)] about the derivation of sharp Sobolev type inequalities in \({\mathbb R}^n\) by means of mass transport methods. The goal of the present paper is to consider three different kinds of extensions of previous results: (1) with trace term in Lipschitz domains, (2) limit inequalities such as trace Faber-Krahn inequalities, trace \(L^p\)-logarithmic Sobolev inequalities and trace Moser-Trudinger inequalities, (3) inequalities on angular domains for which the trace term disappears.
reviewed by: Leszek Skrzypczak
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 35R45
zbMATH DE Number: 5215538
zbMATH Keywords: Sobolev inequalities
zbMATH Keywords: Gagliardo-Nirenberg inequalities
zbMATH Keywords: Faber-Krahn inequalities
zbMATH Keywords: logarithmic Sobolev inequalities
zbMATH Keywords: Moser-Trudinger inequalities
zbMATH Keywords: mass transport methods
MaRDI profile type: Publication
full work available at URL: s00526-007-0105-x
OpenAlex ID: W2081060500
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DOI: 10.1007/S00526-007-0105-X
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