Moser--Trudinger inequality for functions with mean value zero
type: Item
instance of: scholarly article
title: Moser--Trudinger inequality for functions with mean value zero
zbMATH Open document ID: 1138.46026
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-04-19T00:00:00Z
review text: The present paper is devoted to the Moser--Trudinger inequality for functions with mean value zero. The author shows that \[ \sup\Biggl\{\int_\Omega e^{\alpha|u|^{{d\over d-1}}}\,dx : u\in H^{1,d}(\Omega),\;\int_\Omega |\nabla u|^d \,dx= 1,\;\int_\Omega u\,dx= 0\Biggr\} \] is attained for any \(\alpha\leq \alpha_d= d({\omega_{d-1}\over 2})^{{1\over d-1}}\), and the supremum is infinite for any \(\alpha> \alpha_d\), where \(\omega_{d-1}\) is the area of the unit sphere in \(\mathbb{R}^d\) and \(\Omega\) is a bounded domain in \(\mathbb{R}^d\) \((d\geq 2)\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 5144903
zbMATH Keywords: Moser-Trudinger inequality
zbMATH Keywords: blow-up analysis
zbMATH Keywords: extremal function
author: Yunyan Yang
MaRDI profile type: Publication
full work available at URL: j.na.2006.04.004
OpenAlex ID: W1966786070
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DOI: 10.1016/J.NA.2006.04.004
description: scientific article; zbMATH DE number 5144903