The Infinity-Laplacian in Smooth Convex Domains and in a Square

2023/01/21 by Brustad, Karl K., Lindgren, Erik, Lindqvist, Peter · 1 citation
#35J65 #35J94 #35P30 #49N60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.09022

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.

Cited by

• Adaptive Crouzeix-Raviart finite elements for the first eigenpair of p-Laplacian

Related

• The Infinity-Potential in the Square
• On ∞-Ground States in the Plane
• Infinity-Harmonic Potentials and Their Streamlines
• On the boundary Hölder regularity for the infinity Laplace equation
• The Gradient Flow of Infinity-Harmonic Potentials