AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Mathematics in Engineering Article
PDF (379.9 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Poincaré inequalities and Neumann problems for the variable exponent setting

David Cruz-Uribe1( ), Michael Penrod1, Scott Rodney2
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
Department of Mathematics, Physics and Geology, Cape Breton University, Sydney, NS B1M1A2, CA
Show Author Information

Abstract

In an earlier paper, Cruz-Uribe, Rodney and Rosta proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate p-Laplacian. Here we prove a similar equivalence between Poincaré inequalities in variable exponent spaces and solutions to a degenerate p ( ⋅ ) -Laplacian, a non-linear elliptic equation with nonstandard growth conditions.

Keywords

degenerate Sobolev spacesp-LaplacianPoincaréinequalitiesvariable exponentnonstandard growth conditions

References

【1】
【1】
 
 
Crossref Google Scholar
Mathematics in Engineering
Volume 4 Issue 5,
October 2022
Pages 1-22
DOI: 10.3934/mine.2022036

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Cruz-Uribe D, Penrod M, Rodney S. Poincaré inequalities and Neumann problems for the variable exponent setting. Mathematics in Engineering, 2022, 4(5): 1-22. https://doi.org/10.3934/mine.2022036

13

Views

1

Downloads

8

Crossref

2

Web of Science

9

Scopus
Received: 10 April 2021
Accepted: 17 August 2021
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)