\(L^{\infty }\)-estimates for Sobolev functions in terms of \(\nabla \) and \(\Delta \)
type: Item
instance of: scholarly article
title: \(L^{\infty }\)-estimates for Sobolev functions in terms of \(\nabla \) and \(\Delta \)
zbMATH Open document ID: 1183.46034
author: Noboru Okazawa
published in: Mathematische Zeitschrift
publication date: 2009-06-22T00:00:00Z
review text: The author presents several inequalities of the form \[ \|u\|_{L^\infty}^p \leq C \|\Delta^k u\|^{p-\alpha}_p \|\nabla(\Delta^l u)\|^{\alpha}_p \text{ for all }u\in C_c^m({\mathbb R}^n), \] where \(k,l \in {\mathbb N}\cup \{0\}\) are determined by \(m\). If \(p = 2\), the estimates are given with explicit constants; for \(p \neq 2\), explicit constants are obtained in two simple cases.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 5566972
zbMATH Keywords: Sobolev functions
zbMATH Keywords: interpolation inequality
zbMATH Keywords: explicit constant
MaRDI profile type: Publication
full work available at URL: s00209-008-0384-8
OpenAlex ID: W1977135799
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DOI: 10.1007/S00209-008-0384-8
description: scientific article; zbMATH DE number 5566972