Infinity-harmonic potentials and their streamlines

Erik Lindgren; Peter Lindqvist

doi:10.3934/dcds.2019192

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2019, Volume 39, Issue 8: 4731-4746. Doi: 10.3934/dcds.2019192

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Infinity-harmonic potentials and their streamlines

Erik Lindgren^1, , and
Peter Lindqvist^2,

1.
Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden
2.
Department of Mathematical Sciences, Norwegian University of Science and Technology, N–7491, Trondheim, Norway

^* Corresponding author: Erik Lindgren
^* Corresponding author: Erik Lindgren

Received: October 2018

Revised: February 2019

Published: May 2019

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Abstract

We consider certain solutions of the Infinity-Laplace Equation in planar convex rings. Their ascending streamlines are unique while the descending ones may bifurcate. We prove that bifurcation occurs in the generic situation and as a consequence, the solutions cannot have Lipschitz continuous gradients.

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Mathematics Subject Classification: Primary: 49N60, 35J15, 35J60, 35J65, 35J70.

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Figure 1. The streamlines of $ V_\infty $ when $ \Omega $ is the square $ -1<x_1<1,\,\,-1<x_2<1 $

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