The Poincaré inequality and \(p\)-connectedness of a stratified set
type: Item
instance of: scholarly article
title: The Poincaré inequality and \(p\)-connectedness of a stratified set
zbMATH Open document ID: 1411.26019
DOI: 10.1134/S003744661806006X
author: O. M. Penkin
author: N. S. Dairbekov
author: Lyazzat Sarybekova
published in: Siberian Mathematical Journal
publication date: 2019-03-13T00:00:00Z
review text: Extensions of the Poincaré inequality to functions of Sobolev type on a stratified set are derived, proved and discussed. It is shown that the integrability exponents in these analogs of the Poincaré inequality depend on the geometric characteristics of the stratified set. As an application of the Poincaré inequality, the authors prove the solvability of boundary value problems for the \(p\)-Laplacian with boundary conditions of Neumann or Wentzel type. Many examples are included to demonstrate the obtained results.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 7035747
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: stratified set
zbMATH Keywords: \(p\)-Laplacian
MaRDI profile type: Publication
cites work: Connectedness and homogenization. Examples of fractal conductivity
cites work: Strong stratified sets and the Friedrichs inequality
cites work: Q5599495
cites work: Q4073917
cites work: Q4001834
cites work: Q4664614
full work available at URL: s003744661806006x
OpenAlex ID: W2906325240
description: scientific article; zbMATH DE number 7035747