Poincaré-type inequalities for the homotopy operator with \(L^{\varphi }(\varOmega )\)-norms
type: Item
instance of: scholarly article
title: Poincaré-type inequalities for the homotopy operator with \(L^{\varphi }(\varOmega )\)-norms
zbMATH Open document ID: 1234.35009
author: Shusen Ding
author: Jian-Min Zhu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-06-01T00:00:00Z
review text: Based on the notion of \(L^s \) averaging domains defined by \textit{S. G. Staples} [in: Proceedings of the international conference on differential and difference equations and their applications, Melbourne, FL, USA, 2005. New York: Hindawi Publishing Corporation. 1041--1048 (2006; Zbl 1129.43005)], the first author extended the space \(L^s(\Omega)\) to the Orlicz space in [Comput. Math. Appl. 47, No.~10--11, 1611--1618 (2004; Zbl 1063.30022); Proc. Am. Math. Soc. 132, No.~8, 2367--2375 (2004; Zbl 1127.35021)]. With the aid of this notion, the Poincaré inequality for the homotopy operator on the space \(L^\varphi(\Omega)\) is extended.
Mathematics Subject Classification ID: 35A23
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 58A10
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 5903375
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: \(A\)-harmonic equation
zbMATH Keywords: differential forms
zbMATH Keywords: Orlicz space
zbMATH Keywords: averaging domains
reviewed by: Kung Ching Chang
MaRDI profile type: Publication
full work available at URL: j.na.2011.03.018
OpenAlex ID: W2054715308
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DOI: 10.1016/J.NA.2011.03.018
description: scientific article; zbMATH DE number 5903375