Affine Moser-Trudinger and Morrey-Sobolev inequalities
type: Item
instance of: scholarly article
title: Affine Moser-Trudinger and Morrey-Sobolev inequalities
zbMATH Open document ID: 1202.26029
author: Andrea Cianchi
author: Erwin Lutwak
author: Deane Yang
author: Gaoyong Zhang
published in: Calculus of Variations and Partial Differential Equations
publication date: 2010-01-08T00:00:00Z
review text: With the standard \(\mathcal L^p\) energy of gradient replaced by an affine energy, by utilizing the rapidly evolving \(\mathcal L^p\) Brunn-Minkowski theory of Convex Geometry, in particular a recently established affine isoperimetric inequality for convex bodies, an affine version of the euclidean Moser-Trudinger inequality is established. By simple comparison of the affine energy and the \(\mathcal L^p\) energy of gradient, it is noted that this new affine version of Moser-Trudinger inequality is stronger than the euclidean one.
reviewed by: Wing-Sum Cheung
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 5655363
zbMATH Keywords: Moser-Trudinger inequality
zbMATH Keywords: Brunn-Minkowski theory
zbMATH Keywords: convex bodies
MaRDI profile type: Publication
full work available at URL: s00526-009-0235-4
OpenAlex ID: W1964075765
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DOI: 10.1007/S00526-009-0235-4
description: scientific article; zbMATH DE number 5655363