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

Karl K. Brustad; Erik Lindgren; Peter Lindqvist; Karl K. Brustad; Erik Lindgren; Peter Lindqvist

doi:10.3934/mine.2023080

Mathematics in Engineering

2023, Volume 5, Issue 4: 1-16. doi: 10.3934/mine.2023080

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

1.
Frostavegen 1691, NO–7633 Frosta, Norway
2.
Department of Mathematics, KTH – Royal Institute of Technology, 100 44, Stockholm, Sweden
3.
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491, Trondheim, Norway

Received: 25 January 2023 Revised: 20 February 2023 Accepted: 20 February 2023 Published: 22 March 2023
MSC : 35J65, 35J94, 35P30, 49N60

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.
- the infinity-Laplace operator,
- nonlinear eigenvalue problem,
- convex plane domains,
- gradient flow,
- Alexandroff's moving plane
Citation: Karl K. Brustad, Erik Lindgren, Peter Lindqvist. The infinity-Laplacian in smooth convex domains and in a square[J]. Mathematics in Engineering, 2023, 5(4): 1-16. doi: 10.3934/mine.2023080

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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.

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