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 (695.3 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

The infinity-Laplacian in smooth convex domains and in a square

Karl K. Brustad1, Erik Lindgren2( ), Peter Lindqvist3
Frostavegen 1691, NO–7633 Frosta, Norway
Department of Mathematics, KTH – Royal Institute of Technology, 100 44, Stockholm, Sweden
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491, Trondheim, Norway
Show Author Information

Abstract

We extend some theorems for the infinity-ground state and for the infinity-potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent explicit solution disproves a conjecture.

Keywords

the infinity-Laplace operatornonlinear eigenvalue problemconvex plane domainsgradient flowAlexandroff's moving plane
CLC number: 35J65, 35J94, 35P30, 49N60

References

【1】
【1】
 
 
Crossref Google Scholar
Mathematics in Engineering
Volume 5 Issue 4,
August 2023
Pages 1-16
DOI: 10.3934/mine.2023080

{{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:
Brustad KK, Lindgren E, Lindqvist P. The infinity-Laplacian in smooth convex domains and in a square. Mathematics in Engineering, 2023, 5(4): 1-16. https://doi.org/10.3934/mine.2023080

10

Views

1

Downloads

3

Crossref

1

Web of Science

2

Scopus
Received: 25 January 2023
Revised: 20 February 2023
Accepted: 20 February 2023
Published: 15 August 2023
©2023 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)