Poincaré-type inequalities for the composite operator in \(L^{\mathcal{A}}\)-averaging domains
type: Item
instance of: scholarly article
title: Poincaré-type inequalities for the composite operator in \(L^{\mathcal{A}}\)-averaging domains
zbMATH Open document ID: 1479.47038
DOI: 10.1155/2014/675464
author: Guannan Shi
author: Yuming Xing
author: Baiqing Sun
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We first establish the local Poincaré inequality with \(L^{\mathcal{A}}\)-averaging domains for the composition of the sharp maximal operator and potential operator, applied to the nonhomogenous \(A\)-harmonic equation. Then, according to the definition of \(L^{\mathcal{A}}\)-averaging domains and relative properties, we demonstrate the global Poincaré inequality with \(L^{\mathcal{A}}\)-averaging domains. Finally, we give some illustrations for these theorems.
Mathematics Subject Classification ID: 47G40
Mathematics Subject Classification ID: 58A10
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 7022859
zbMATH Keywords: local Poincaré inequality
zbMATH Keywords: nonhomogenous \(A\)-harmonic equation
zbMATH Keywords: \(L^{\mathcal{A}}\)-averaging domains
Wikidata QID: Q59040509
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/675464
OpenAlex ID: W1972738556
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description: scientific article; zbMATH DE number 7022859