Extremals for Moser inequalities
type: Item
instance of: scholarly article
title: Extremals for Moser inequalities
zbMATH Open document ID: 1092.46023
author: Yanyan Li
published in: Archive for Rational Mechanics and Analysis
publication date: 2004-09-22T00:00:00Z
review text: The authors show that for Moser-Trudinger inequalities \[ \int_Q|\nabla u|^2 \,d\mu\leq 1\quad\text{and}\quad \int_Q u\,d\mu= 0, \] where \(\nabla u\) is the gradient with respect to the usual metric on the sphere and \(d\mu\) the corresponding volume element, there exists an extreme solution involving exponential integrals. The results are obtained for Sobolev spaces when the domain \(Q\) is one of the spheres \(S^2\) and \(S^3\), the unit disk \(Q= D^2\) or the projective space \(\mathbb RP^2\). The method of Carleson and Chang is used for \(n\)-balls, with boundary value zero modified, and applied to functions with mean value zero on these domains. This approach also provides an elementary proof of the Moser inequality for \(S^n\), \(n\geq 2\), which is a special case of the result of Fortuna.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 2101868
zbMATH Keywords: Moser inequality
zbMATH Keywords: Sobolev space
zbMATH Keywords: exponential integral
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
full work available at URL: s00205-003-0280-7
OpenAlex ID: W2089252160
DOI: 10.1007/S00205-003-0280-7
description: scientific article; zbMATH DE number 2101868