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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
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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

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

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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

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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)