On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces
type: Item
instance of: scholarly article
title: On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces
zbMATH Open document ID: 1404.46036
zbMATH Open document ID: 1441.46029
DOI: 10.4171/RLM/808
DOI: 10.1007/S11854-019-0029-3
author: Enea Parini
author: Bernhard Ruf
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
published in: Journal d'Analyse Mathématique
publication date: 2018-07-02T00:00:00Z
publication date: 2019-10-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1607.07681
review text: Summary: We give a contribution to the problem of finding the optimal exponent in the Moser-Trudinger inequality in the fractional Sobolev-Slobodeckij space \(\tilde{W}^{s,p}_0(\Omega)\), where \(\Omega\subset\mathbb{R}^N\) is a bounded domain, \(s\in(0,1)\), and \(sp=N\). We exhibit an explicit exponent \(\alpha^\ast_{s,N}>0\), which does not depend on \(\Omega\), such that the Moser-Trudinger inequality does not hold true for \(\alpha\in(\alpha^\ast_{s,N},+\infty)\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35A23
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 6898071
zbMATH DE Number: 7121336
zbMATH Keywords: fractional Moser-Trudinger inequality
zbMATH Keywords: fractional Sobolev space
zbMATH Keywords: optimal exponent
zbMATH Keywords: Moser-Trudinger inequality
zbMATH Keywords: Sobolev-Slobodeckij spaces
MaRDI profile type: Publication
arXiv ID: 1607.07681
OpenAlex ID: W2964320629
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Wikidata QID: Q127595436
description: scientific article; zbMATH DE number 7121336